Nonsingular Solutions Research Articles

Novel complexiton, rational wave, multi-lumps and the kink solitary wave solutions to the new (3+1)-dimensional integrable fourth-order equation for shallow water waves

In this exploration, we aim to seek a number of new exact solutions to the new (3+1)-dimensional integrable fourth-order nonlinear equation, which is widely used to describe the shallow water waves. Employing the Cole-Hopf transformation, we develop its bilinear form. Then, taking advantage of the ansatz function method, a new functional form is utilized to probe the singular complexiton solutions. Based on which, the non-singular complexiton solutions are derived by imposing the constraint conditions. In addition, we find the rational wave solutions and multi-lumps solutions wielding the rational function method and new homoclinic method respectively. At the end, we investigate the kink solitary wave solutions using the variational approach that is based on the variational principle and Ritz method. Meanwhile, the Hamiltonian of the system is also elaborated. Correspondingly, the graphic descriptions of the extracted results are presented to unfold their dynamic behaviors through Maple. As we all know, the findings of this paper are firstly reported and can enlarge the exact solutions of the considered PDE.

Large D gravity and low D string via α′ corrections

In this paper, we generalize the correspondence between large D gravity and low D string theory to the most general case, including its T-dual solutions. It is well-known that the large D limit of the Schwarzschild-Tangherlini black hole in gravity becomes a two-dimensional near-horizon geometry. Similarly, the large D limit of its T-dual solution, obtained by the Buscher rules, namely the string black hole with a naked singularity, reduces to a two-dimensional near-singularity geometry. Both of these geometries are described by the two-dimensional low-energy effective action of string theory and are related to each other by scale-factor duality. Secondly, we demonstrate that these near-horizon/singuglarity geometries, including complete α′ corrections, can be described by the two-dimensional Hohm-Zwiebach action. This approach allows for the derivation of non-perturbative and non-singular solutions. Furthermore, the Hohm-Zwiebach action provides a systematic way to investigate the α′-corrected near-horizon/singularity geometries of different kinds of black holes, which are difficult to achieve through the Wess-Zumino-Witten (WZW) model method.

Bose–Einstein Condensation dark matter models generated by gravitational decoupling

A study on massive compact objects influenced by Bose–Einstein condensation (BEC) dark matter (DM) with a gravitational decoupling approach is presented within the context of f(Q) gravity, assuming a linear form of f(Q). In order to obtain physically valid solutions to the basic field equations of the decoupled systems, we take the Tolman IV potential ansatz for the seed system and the BEC-DM density profile for the new source into consideration. After that, we apply the boundary conditions on the decoupled system with Schwarzschild-de Sitter spacetime as the exterior metric. Eventually, we obtain a complete non-singular solution to the decoupled system, consisting of a strange stellar configuration with a BEC-DM density profile. All the physical properties, such as the effective energy density, pressure along the radial as well as the tangential direction, and anisotropy in the system, are rigorously investigated. Analyzing the stability conditions of the decoupled stellar configuration, we study mass–radius (M−R) relations with observational constraints related to the supermassive compact stars, such as PSR J0740+6620, PSR J2215+5135, GW190814, and GW200210, with observed masses larger than or equal to 2 M⊙. Notably, we examine the influence of DM on constraining the M−R measurements of the observed stars, which satisfy the MIT bag model equation of state as well as the condition of mimicking, i.e., ρθ=ρDM, in the background of f(Q) gravity. Interestingly, any possible conversion of massive compact stars to smaller black holes can be restrained, as the presence of a DM halo in the strange stellar system reduces the maximum mass effectively, as indicated by the M−R curves. This result regarding the maximum mass of the compact star can be associated with the astrophysical data concerning the mass gap of the events GW190814 and GW200210. Specifically, the present model predicts the radius for PSR J0740+6620 as 13.69−0.10+0.09 km, which nearly matches the NICER and XMM-Newton data.

Stability and viability of charged anisotropic pulsar SAX J1748.9-2021 in extended symmetric teleparallel gravity

This manuscript aims to study the viability and stability of a pulsar SAX J1748.9-2021, containing a charged anisotropic matter configuration within the framework of f(Q,T) theory (Q and T are the non-metricity scalar and energy–momentum tensor, respectively). We employ a non-singular solution and a specific model of this gravitational theory and use junction conditions to determine the unknown constants in the metric coefficients. We explore different geometric and physical properties using astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. This framework establishes relationships between various physical quantities, including fluid parameters, anisotropy, mass–radius relation, redshift, the Zeldovich condition, energy conditions, causality conditions, adiabatic index, Tolman–Oppenheimer–Volkoff equation, equation of state parameter and compactness. Our findings affirm the feasibility and stability of the proposed charged pulsar within this theoretical framework.

A comprehensive analysis of charged pulsars and cracking condition

The main aim of this manuscript is to analyze the viability and stability of pulsars filled with charged anisotropic matter configuration in extended symmetric teleparallel theory. A particular model of this gravitational theory is considered to reduce the complexity of the system and formulate the explicit field equations which govern the interaction between matter and geometry. The configuration of static spherical symmetric structures is examined through the non-singular viable solutions. The undetermined constants in the metric coefficients are determined by the Darmois junction conditions. Further, we explore different physical characteristics in the interior of charged pulsars to check their viability. The equilibrium state of the charged stellar objects is discussed using the Tolman–Oppenheimer–Volkoff equation and the stability is examined by the causality condition, Herrera cracking approach and adiabatic index, respectively. Our findings indicate that the proposed charged stars in this modified gravity are physically viable and stable.

Existence of non-singular stellar solutions within the context of electromagnetic field: a comparison between minimal and non-minimal gravity models

In this paper, we explore the existence of various non-singular compact stellar solutions influenced by the Maxwell field within the matter-geometry coupling based modified gravity. We start this analysis by considering a static spherically symmetric spacetime which is associated with the isotropic matter distribution. We then determine the field equations corresponding to two specific functions of this modified theory. Along with these models, we also adopt different forms of the matter Lagrangian. We observe several unknowns in these equations such as the metric potentials, charge and fluid parameters. Thus, the embedding class-one condition and a particular realistic equation of state is used to construct their corresponding solutions. The former condition provides the metric components possessing three constants, and we calculate them through junction conditions. Further, four developed models are graphically analyzed under different parametric values. Finally, we find all our developed solutions well-agreeing with the physical requirements, offering valuable insights for future explorations of the stellar compositions in this theory.

Stability analysis of charged neutron stars and Darmois junction conditions

This research article examines the impact of f(Q,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {Q}},{\\mathcal {T}})$$\\end{document} theory on the geometry of charged neutron stars filled with anisotropic matter configuration. Here, Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {Q}}$$\\end{document} represents non-metricity and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {T}}$$\\end{document} denotes the trace of energy-momentum tensor. We use a particular functional form of this modified theory to reduce the system’s complexity and derive explicit relations of the energy density and pressure components. Further, we consider viable non-singular solutions to analyze the internal structure of the charged neutron stars. The unspecified parameters in the metric coefficients are evaluated through Darmois junction conditions, which ensures consistency between interior and exterior solutions of the stellar objects. These parameters are then used to explore different physical characteristics such as the behavior of energy density, pressure components, anisotropy, energy bounds, equation of state parameter, compactness and redshift function in the interior of charged neutron stars. The stability and equilibrium states of the charged stellar objects are discussed using the Tolman–Oppenheimer–Volkoff equation and the speed of sound, respectively. Our results suggest that the charged neutron stars are viable and stable in the presence of dark source terms.

Effect of torsion and electric charge parameters on the configuration of anisotropic compact stars in [formula omitted] gravity

Under the assumption of a linear f(T) function, we present a new exact solution for an anisotropic and charged stars in the background of f(T)-gravity. By considering ansatz for the metric potential, charge function, and anisotropy function, we have arrived at an exact and nonsingular solution to the field problem. The anisotropy and charge function are discovered to be contingent upon the existence of the torsion scalar, and the evolution of the charge and anisotropy of the stellar matter is significantly influenced by variations in the torsion parameter ζ1. The features of anisotropy and charged compact star at the boundary are examined by making the interior metric solution correspond to the exterior Reissner-Nordström-de Sitter solution. The physical validity of the derived quantities is shown graphically, and the energy conditions are found to be satisfied. The causality condition, hydrostatic stable equilibrium, and adiabatic stability are also verified for the chosen values of the torsion parameter. The M−R relations are analyzed for the charged and anisotropic stellar configurations in f(T)-gravity. It is found that increasing values of the torsion parameter ζ1 enhance the maximum mass of the star while increasing values of the charge parameter q0 decrease the maximum mass. The influence of anisotropy via increasing the torsion parameter could be a probable interpretation of the maximum masses exceeding 2.5 M⊙, as observed in the case of the secondary companion of GW190814. Interestingly, our study sheds light on the characteristic of non-singular solutions to the field equations in f(T)-gravity with linear f(T).

Healthy Horndeski cosmologies with torsion

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the ℒ5 part of the Horndeski action (Gμν ∇ μ ∇ νϕ, and (∇2 ϕ)3). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies.

Novel complexiton solutions to the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for incompressible fluid

This letter focuses on exploring some novel exact solutions to the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) that has a major role in incompressible fluid. Adopting the Cole-Hopf transformation, the bilinear form of the considered equation is successfully constructed. Then the singular complexiton solutions (SCSs) are developed by applying the ansatz function method with a novel functional form. Additionally, we also find the non-singular complexiton solutions (NCSs) via imposing the restrictive conditions. To unveil the behaviors of the attained solutions better, the corresponding outlines are plotted via Maple.

Non-oscillatory fracture mode partition for interface crack under mixed-mode loading

The oscillatory crack-tip field in the classical interface fracture mechanics solution often leads to complications in identifying the mode mixity in bimaterial interface fracture problems. In this paper, a non-singular series solution for the continuum problem of a crack on the cohesive-spring interface under mixed-mode loading is presented and compared to the classical oscillatory solution. A Gaussian process regression model was also developed to enable quick evaluation of the phase angle for interface delamination characterization by using mixed-mode bending fracture test.

Charged gravastars with conformal motion in the Finslerian space-time

In this article, we investigate the charged gravastar under conformal motion with the background of Finsler geometry. Mazur and Mottola pioneered the concept of the gravastar (gravitational vacuum star) for the first time. This vacuum object consists of three distinct regions, that is, (i) interior de Sitter region, (ii) thin shell consisting of ultrarelativistic stiff, and (iii) exterior vacuum Schwarzschild region. The nature of these regions can be analyzed by considering different equations of state parameters. We have studied various physical features of the gravastar, such as length, energy, entropy, stability, and the adiabatic index, both graphically and analytically within the Finslerian framework. Also, we have obtained the exact and non-singular solution for the gravastar model.

Families of propagating soliton solutions for (3+1)-fractional Wazwaz-BenjaminBona-Mahony equation through a novel modification of modified extended direct algebraic method

The article presents a new modification to the modified Extended Direct Algebraic Method (mEDAM) namely r+mEDAM to effectively and precisely acquire propagating soliton and other travelling wave solutions to the Fractional Wazwaz-Benjamin-Bona-Mahony (FWBBM) equation. By using this updated approach, we are able to find more and new families of propagating soliton solutions for the FWBBM problem, such as soliton, kink, lump-like singular, trigonometric, hyperbolic, periodic, shock, singular & non-singular wave solutions. We also provide 3D and 2D graphs that visually illustrate the obtained solutions. By obtaining accurate propagating soliton solutions, our r+mEDAM proves to be practical while also revealing important details about the dynamics of the equation and suggesting possible applications in the fields of optics, materials research, and water waves.

Global phase space analysis for a class of single scalar field bouncing solutions in general relativity

We carry out a compact phase space analysis of a non-canonical scalar field theory whose Lagrangian is of the form F(X)-V(ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)-V(\\phi )$$\\end{document} within general relativity. In particular, we focus on a kinetic term of the form F(X)=βXm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)=\\beta X^m$$\\end{document} (m≠1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ e 1/2$$\\end{document}) with power-law potential V0ϕn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_0 \\phi ^n$$\\end{document} and exponential potential V0e-λϕ/MPl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_0 e^{-\\lambda \\phi /M_{Pl}}$$\\end{document} of the scalar field. The Cuscuton case m=1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1/2$$\\end{document} where the scalar field is non-dynamical is left out of consideration. The main aim of this work is to investigate the genericity of nonsingular bounce in these models and to investigate the cosmic future of the bouncing cosmologies when they are generic. A global dynamical system formulation that is particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. We show that when F(X)=βXm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)=\\beta X^m$$\\end{document} (β<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta <0$$\\end{document}), nonsingular bounce is generic for a power law potential V(ϕ)=V0ϕn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\phi ) = V_0 \\phi ^n$$\\end{document} only within the parameter range 12<m<1,n<2mm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{1}{2}<m<1,\\,n<\\frac{2\\,m}{m-1}\\right\\} $$\\end{document} and for an exponential potential V(ϕ)=V0e-λϕ/MPl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\phi ) = V_0 e^{-\\lambda \\phi /M_{Pl}}$$\\end{document} only within the parameter range 12<m≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{1}{2}<m\\le 1\\right\\} $$\\end{document}. Except in these cases, nonsingular bounce in these models is not generic due to the non-existence of global past or future attractors. Our analysis serves to show the importance of a global phase space analysis to address important questions about nonsingular bouncing solutions, an idea that may and must be adopted for such solutions even in other theories.

Singularity free cosmological models in viscous symmetric teleparallel gravity

In this paper, we have investigated the possibility of deriving exact non-singular cosmological solutions in a combined scenario of bulk viscous fluid and symmetric teleparallel gravity (f(Q) gravity). Interestingly, we have found that the general solutions obtained from our models are flexible enough for demonstrating the emergent Universe scenario, inflation and late-time dark-energy-like behaviour. We have found that these phases of the Universe depend crucially on the viscosity parameters ζ0, ζ1 considered in this work and also the parameter n associated with the f(Q) model. Hence, we performed an analysis concerning the model’s relevance with the observed data to constrain the aforementioned parameters.

Evaluation of mixed-mode stress intensity factors for anisotropic elastic solids with interface singularity

Abstract When a structure is composed of many different parts and each part is made of different materials, it is very possible that many interface corners appear in several local fields of the structure. Due to the mismatch of elastic properties, stress singularity may occur at the interface corners. The singular orders of stresses and their associated stress intensity factors (SIFs) are two important parameters for understanding failure initiation. Since the singular orders of general interface corners may be real or complex, distinct or repeated, several different definitions of SIFs have been proposed for different types of interfaces. In order to build a direct connection among all general interface corners (including cracks and interface cracks), a unified definition of SIFs was proposed in our previous studies. To calculate the uni-defined SIF accurately and efficiently, a special boundary element using the fundamental solution satisfying interface continuity conditions is established. The singular integrals involved in the associated boundary integral equations are solved by the setting of proper rigid body motions and the approximation through interpolation of nearby non-singular solutions. To avoid the unstable and inaccurate region near the corners, in this study we employ the path-independent H-integral, and derive the relations between H-integral and SIFs. Moreover, the auxiliary solutions of displacements and tractions required in the H-integral are provided for different integral paths. Several numerical examples, such as interface cracks, interface corners, single lap joints and delamination, are presented to demonstrate the methodology employed in this paper.

Neutron stars with polytropic equation of state

In this work, the neutron star model is considered in the framework of general relativity with the polytropic equation of state p=ργ, where γ=1+1k and k is known as a polytropic index. The homotopy perturbation method is used to solve Tolman–Oppenheimer–Volkoff (TOV) equation which gives the mass of the stellar structure. The solution of Einstein’s field equations is obtained and stability, causality, and physical viability of the considered model are examined. Using the observational results of mass and radius of known stars 4U 1608-52 RX J185635-3754, SAX J1748.9-2021 and 4U 1728-34, the model parameters are estimated which led to the non-singular solutions satisfying the energy conditions.

An improved localized boundary knot method for 3D acoustic problems

In this paper, an improved localized boundary knot method (LBKM) is proposed for 3D acoustic problems. The domain is divided into many small subdomains, and the solutions at the nodes of each subdomain are approximated by using the linear combination of the non-singular general solutions in the LBKM. However, the interpolant matrix generation for each subdomain in the original LBKM is associated with the variables at both domain and boundary nodes. In the present method, only the variables at domain nodes are considered for the matrix generation, and the boundary conditions are directly imposed during the matrix generation. As a consequence, the computational efficiency of the LBKM should be raised. Two examples are provided to illustrate the performance of the present method.

Laminar hypersonic boundary layer flow over planar compression ramp with sharp leading edge and upstream influence

The present work aims to study the effects of shock wave — boundary layer interaction in 2D hypersonic flow at the sharp leading edge of a flat plate and a flat plate followed by a compression ramp. A key parameter in this work is the hypersonic interaction parameter χ, defined as χ≡CM∞3/Re∞1/2. This flow is modeled as a perfect gas and its behavior is studied over various compression ramp configurations, ranging from 0°–6°, using a semi-analytic reduced-order model. In this shock-layer analysis we focus on characterizing the viscous boundary layer for an adiabatic flow over an insulated wall, improving on existing semi-analytic methods by obtaining a non-singular solution, and using the Tangent Wedge approximation to match the pressure on the boundary layer edge. Upstream influence resulting from the compression ramp is also investigated with newly developed correlations.

’t Hooft–Polyakov monopoles and a general spherically symmetric solution of the Bogomolny equations

In this paper, we briefly review the ’t Hooft–Polyakov monopoles and the Bogomolny equations providing minimal energy field configurations in each topologically distinct sectors of monopole solutions. Then we consider the most general spherically symmetric ansatz for gauge fields depending on three arbitrary functions and find a general spherically symmetric solution of the Bogomolny equations. It depends on two integration constants and one arbitrary function on radius. The arbitrary function is proved to be related to the residual gauge symmetry of field configurations. In a general case, the spherically symmetric Euler–Lagrange equations are reduced to two nonlinear field equations for the two invariant functions. The Bogomolny–Prasad–Sommerfield solution is proved to be the only spherically symmetric nonsingular solution of field equations with finite energy.