Non-topological Soliton Solutions Research Articles

Exact solutions, wave dynamics and conservation laws of a generalized geophysical Korteweg de Vries equation in ocean physics using Lie symmetry analysis

An evolution equation is a partial diferential equation that describes the time evolution of a physical system starting from given initial data. Evolution equations arise from many areas of applied and engineering sciences. To this end, this article investigates the analytical studies of a generalized geophysical Korteweg-de Vries equation in ocean physics. The examination of this model is conducted via the Lie group theory of diferential equations. In the first place, point symmetries, which are constituent elements of a four-dimensional Lie algebra, are systematically computed. Thereafter, one-parameter transformation groups for the algebra are calculated. Besides, going forward, a one-dimensional optimal system of subalgebras is derived in a procedural manner. Sequel to this, the subalgebras and combination of the achieved symmetries are invoked in the reduction proces which enables the derivation of nonlinear ordinary diferential equations associated with the generalized geophysical Korteweg-de Vries equation under study. Most of the achieved nonlinear ordinary diferential equations are further solved either via direct integration or using a power series approach. Furthermore, travelling wave solutions are initially obtained. This is attained via direct integration and the use of Jacobi elliptic function approach. These techniques enable the attainment of various exact soliton solutions, including non-topological soliton solutions as well as general periodic function solutions of note, such as cosine amplitude, sine amplitude, and delta amplitude solutions of the model. Furthermore, numerical simulations of the solutions are invoked to gain a gross knowledge of the physical phenomena represented by the under-study generalized geophysical Korteweg-de Vries equation in ocean physics. In the end, the investigation further gives attention to the calculation of conserved vectors for the model using Ibragimov's theorem for conservation laws, as well as Noether's theorem.

Skyrmions and pion stars in the gauged U(1) Einstein-Skyrme model

We consider topological and nontopological regular soliton solutions in the Einstein-Maxwell-Skyrme theory. We analyze the properties of these solutions and determine their domains of existence. The dependence of the solutions on the gauge coupling and on the strength of the effective gravitational coupling are examined. Topologically trivial localized field configurations, , are shown to exist, as nonlinear gravitational bound states of the Skyrme field. Both spherically symmetric and axially symmetric pion stars are considered. We find that these solutions share many features with the usual (mini)boson stars. In particular they also exhibit a spiraling behavior and do not possess a flat space limit. Published by the American Physical Society 2024

Traveling Wave Solutions and Conservation Laws of a Generalized Chaffee–Infante Equation in (1+3) Dimensions

This paper aims to analyze a generalized Chaffee–Infante equation with power-law nonlinearity in (1+3) dimensions. Ansatz methods are utilized to provide topological and non-topological soliton solutions. Soliton solutions to nonlinear evolution equations have several practical applications, including plasma physics and the diffusion process, which is why they are becoming important. Additionally, it is shown that for certain values of the parameters, the power-law nonlinearity Chaffee–Infante equation allows solitons solutions. The requirements and restrictions for soliton solutions are also mentioned. Conservation laws are derived for the aforementioned equation. In order to comprehend the dynamics of the underlying model, we graphically show the secured findings. Hirota’s perturbation method is included in the multiple exp-function technique that results in multiple wave solutions that contain new general wave frequencies and phase shifts.

Non-topological soliton solution of (2+1)-dimensional complex three coupled nonlinear Maccari’s model via modified new Kudryashov scheme

This paper, deals with the (2+1)-dimensional complex three coupled nonlinear Maccari’s model (3-CCME) by utilizing recently presented modified new Kudryashov method (mNKM). The focus of this article is to obtain non-topological soliton solution of 3-CCME by applying mKNM method, which has not been applied before to the investigated problem. Applying the proposed method successfully, besides the non-topological soliton solution of the investigated problem, the breather-like type soliton solution was also obtained and the obtained results are depicted by the 3D, 2D and contour graphical presentations.

Non-topological, topological and rogue wave Soliton solutions for Sharma Tasso Olver equation

This paper proposes three types of envelope solitons for the Sharma-Tasso-Olver equation with power-law nonlinearity. The ansatz approach is used to investigate the presence of these solitons identified during the solution derivation. As a result, we acquired the bright, singular, and dark solitons, which have a wide range of applications in applied science and engineering. Furthermore, the physical structures of the obtained solitons are investigated using two-dimensional, three-dimensional, and three-dimensional revolution plots with varying parameter values.

Stability analysis, symmetry solutions and conserved currents of a two-dimensional extended shallow water wave equation of fluid mechanics

This paper analytically investigates a new (2+1)-dimensional extended shallow water wave equation. Lie group theory along with direct integration is used to achieve some solutions of the equation. The solutions obtained are in terms of Jacobi elliptic function as well as Weierstrass elliptic function. Besides, we apply the He’s variational technique to secure some non-topological soliton solutions of the equation. Series solution of the equation is also achieved by employing power series technique and we show the convergence of the series. Furthermore, graphical exhibitions of the dynamical character of the gained result are presented and discussed in a bid to have a sound understanding of the physical phenomena of the underlying model. In addition, we examine the stability analysis of the equation. Conclusively, we give the conserved currents of the aforementioned equation by employing the homotopy formula together with the Noether theorem.

Solitary waves in magnetostrictive circular rods with temperature effect

A simple nonlinear model is constructed in this paper to study the solitary wave in an infinite circular magnetostrictive rod. Based on the constitutive relations for transversely isotropic magnetostrictive materials, considering the coupling of multiphysics, combined with Hamilton’s principle and Euler equation, the longitudinal wave equation (LWE) of the infinite circular rod is obtained. The nonlinearity considered is geometrically associated with the nonlinear normal strain in the longitudinal rod direction. The transverse Poisson’s effect is included by introducing the effective Poisson’s ratio. Solitary wave solution, non-topological bell-type soliton and singular periodic solutions of the LWE are obtained by the [Formula: see text]-expansion method. By using the reductive perturbation method, we derive the KdV equation, furthermore, the two-solitary solution is obtained. Numerical analysis results show that the increase of the magnetic field intensity or temperature will reduce the solitary wave’s propagation velocity. As the wave velocity ratio increases, the wave amplitude gradually increases; when the coupled physics parameter and the wave velocity ratio are constant, the increase of the dispersion parameter will make the wavelength longer. The dynamic behavior of the two-soliton solution in the magnetostrictive rod exhibits nonlinear superposition and has elastic collision characteristics.

New topological and non-topological unidirectional-wave solutions for the modified-mixed KdV equation and bidirectional-waves solutions for the Benjamin Ono equation using recent techniques

In this paper, new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidirectional waves for the Benjamin Ono equation are studied. New extension of the rational sine-cosine and sinh-cosh methods are used. In addition, an extension of the recent polynomial function method is applied as well. Different types of topological and non-topological soliton solutions are extracted to the proposed models and categorized by providing 2D and 3D graphs. Finally, some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.

Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of lattice solitons. We first briefly review the classical inverse scattering method in the continuum limit, focusing on the Korteweg-de Vries (KdV) equation and SU(N) Gross-Neveu model in the large N limit. We then generalize this methodology to lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities had been known as far back as Toda; however, we derive a new set of identities for the discrete Dirac operator. We then use these identities in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential, the former of which has no analogue in the continuum limit. We explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

Variety of nontopological solitons in a spontaneously broken U(1) gauge theory: Dust balls, shell balls, and potential balls

We show, by numerical calculations, that there exist three-types of stationary and spherically symmetric nontopological soliton solutions (NTS-balls) with large sizes in the coupled system consisting of a complex matter scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneously symmetry breaking. Under the assumption of symmetries, the coupled system reduces to a dynamical system with three degrees of freedoms governed by an effective action. The effective potential in the action has stationary points. The NTS-balls with large sizes are described by bounce solutions that start off an initial stationary point, and traverse to the final stationary point, vacuum stationary point. According to the choice of the initial stationary point, there appear three types of NTS-balls: dust balls, shell balls, and potential balls with respect to their internal structures.

Mapping gauged Q -balls

Scalar field theories with particular U(1)-symmetric potentials contain non-topological soliton solutions called Q-balls. Promoting the U(1) to a gauge symmetry leads to the more complicated situation of gauged Q-balls. The soliton solutions to the resulting set of nonlinear differential equations have markedly different properties, such as a maximal possible size and charge. Despite these differences, we discover a relation that allows one to extract the properties of gauged Q-balls (such as the radius, charge, and energy) from the more easily obtained properties of global Q-balls. These results provide a new guide to understanding gauged Q-balls as well as providing simple and accurate analytical characterization of the Q-ball properties.

Transforming kinks into compactons in the [formula omitted]-sigma model

In this work, we investigate the solutions of vortices in the O(3)-sigma model with the gauge field governed by the Chern–Simons term and subject to a hyperbolic self-dual potential. We show that this model admits both topological and nontopological soliton solutions. Employing numerical analysis, we realize that the topological solutions of the model can be transformed into compacton-like solutions. On the other hand, after modifying the model by the introduction of a dielectric constant, an exciting feature appears; namely, the nontopological solutions can be transformed into kink-like solutions through the numerical variation of the dielectric constant. Furthermore, we discuss the degeneracy for the topological solitons in a given sector. Finally, we present the numerical solutions of the first model.

Stability catalyzer for a relativistic non-topological soliton solution

For a real nonlinear Klein–Gordon Lagrangian density with a special solitary wave solution (SSWS), which is essentially unstable, it is shown how adding a proper additional massless term could guarantee the energetically stability of the SSWS, without changing its dominant dynamical equation and other properties. In other words, it is a stability catalyzer. The additional term contains a parameter B, which brings about more stability for the SSWS at larger values. Hence, if one considers B to be an extremely large value, then any other solution which is not very close to the free far apart SSWSs and the trivial vacuum state, require an infinite amount of energy to be created. In other words, the possible non-trivial stable configurations of the fields with the finite total energies are any number of the far apart SSWSs, similar to any number of identical particles.

New wave behaviors and stability analysis of the Gilson–Pickering equation in plasma physics

This study investigates the Gilson–Pickering equation by using the sine-Gordon expansion method. Sine-Gordon expansion method is one of the most powerful methods for solving the nonlinear partial differential equations. We successfully construct various exact solitary wave solutions to the governing equation, such as shock wave, topological, non-topological, compound topological, and non-topological soliton wave solutions. In addition, the stability of the studied nonlinear equation is analyzed via the linear stability analysis. The 2D, 3D, and contour surfaces are also plotted for all obtained solutions.

Introducing a relativistic nonlinear field system with a single stable non-topological soliton solution in [formula omitted] dimensions

In this paper we present a new extended complex nonlinear Klein–Gordon Lagrangian density, which bears a single non-topological soliton solution with a specific rest frequency ωs in 1+1 dimensions. There is a proper term in the new Lagrangian density, which behaves like a massless spook that surrounds the single soliton solution and opposes any internal changes. In other words, any arbitrary variation in the single soliton solution leads to an increase in the total energy. Moreover, just for the single soliton solution, the general dynamical equations are reduced to those versions of a special type of the standard well-known complex nonlinear Klein–Gordon systems, as its dominant dynamical equations.

The Role of the Massless Phantom Term in the Stability of a Non-Topological Soliton Solution

We intend to introduce classically a special Lagrangian density in such a way that, firstly, it leads to a special non-topological solitary wave solution, secondly, the stability of that is guaranteed properly, and thirdly, its dominant dynamical equations reduce to the standard nonlinear Klein-Gordon equations. For these purposes, we have to consider a new term in the Lagrangian density, whose role is like a massless phantom that surrounds the special solitary wave solution and resists any change in its internal structure.

Homogeneous balls in a spontaneously broken U(1) gauge theory

We study the coupled system consisting of a complex matter scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneously symmetry breaking. We show by numerical calculations that there are spherically symmetric nontopological soliton solutions. Homogeneous balls solutions, all fields take constant values inside the ball and in the vacuum state outside, appear in this system. It is shown that the homogeneous balls have the following properties: charge density of the matter scalar field is screened by counter charge cloud of the Higgs and gauge field everywhere; an arbitrary large size is allowed; energy density and pressure of the ball behave homogeneous nonrelativistic gas; a large ball is stable against dispersion into free particles and against decay into two smaller balls.

Invariant Subspace and Classification of Soliton Solutions of the Coupled Nonlinear Fokas-Liu System

In this work, the coupled nonlinear Fokas–Liu system which is a special type of KdV equation is studied using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the nonlinear partial differential equations (NPDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, polynomial and logarithmic function solutions of the equation are derived. Further more, the ansatz approached is utilized to derive the topological, non-topological and other singular soliton solutions of the system. Numerical simulation off the obtained results are shown.

One-dimensional soliton system of gaugedQ-ball and anti-Q-ball

The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological soliton solutions describing soliton systems consisting of two Q-ball components possessing opposite electric charges. The two Q-ball components interact with each other through the Abelian gauge field and the quartic scalar interaction. The interplay between the attractive electromagnetic interaction and the repulsive quartic interaction leads to the existence of symmetric and nonsymmetric soliton systems. Properties of these systems are investigated by analytical and numerical methods. The symmetric soliton system exists in the whole allowable interval of the phase frequency, whereas the nonsymmetric soliton system exists only in some interior subinterval. Despite the fact that these soliton systems are electrically neutral, they nevertheless possess nonzero electric fields in their interiors. It is found that the nonsymmetric soliton system is more preferable from the viewpoint of energy than the symmetric one. Both symmetric and nonsymmetric soliton systems are stable to the decay into massive scalar bosons.

Charge-screened nontopological solitons in a spontaneously broken U(1) gauge theory

We construct, numerically, stationary and spherically symmetric nontopological soliton solutions in the system composed of a complex scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneous symmetry braking. It is shown that the charge of the soliton is screened by counter charge everywhere.