Boiti Leon Manna Pempinelli Equation Research Articles

Lax integrability and infinite superposition solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Lax integrability and infinite superposition solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

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.

Soliton molecules and the novel hybrid interaction solutions of the new extended (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Soliton molecules and the novel hybrid interaction solutions of the new extended (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Dispersive soliton solutions to the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation via an analytical method

Dispersive soliton solutions to the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation via an analytical method

Superposition Formula of arbitrary functions to a (3+1)-demensional Boiti–Leon–Manna–Pempinelli equation

The (3+1)-dimensional Boiti–Leonon–Manna–Pempinelli equation was studied by using Hirota bilinear method. In this paper, we successfully derived the multi-solutions of this equation consisting of the superpositions of M arbitrary functions. A variety of new solutions can be obtained by choosing different values of the parameter M and test functions f in this paper, i.e., the localized solutions generated by M-positive quadratic functions, the mixed solutions consisting of the localized wave solutions and the kink wave solutions, and the mixed solutions consisting of a trigonometric function and exponential functions. Meanwhile, their corresponding physical plots were displayed to analyze their physical significance and dynamic properties. Some solutions from previous studies were found when M took a specific value and the test functions took particular functions. Thus, the received solutions are more general compared to the previous studies.

Multi-wave complexiton, multi-wave, interaction-wave and the travelling wave solutions to the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation for the incompressible fluid

Multi-wave complexiton, multi-wave, interaction-wave and the travelling wave solutions to the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation for the incompressible fluid

Rational solutions consisting of multiple lump waves and line rogue waves in different spaces of the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

Rational solutions consisting of multiple lump waves and line rogue waves in different spaces of the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

The central target of this work is to extract some novel exact solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) for the incompressible fluid. By applying the weight algorithm (WA) and linear superposition principle (LSP), we construct two sets of the complexiton solutions, which are the non-singular complexiton and singular complexiton solution via introducing the pairs of the conjugate parameters. In addition, we also explore the complex N-soliton solutions (CNSSs) via the Hirota bilinear equation (HBE) that is developed by the Cole-Hopf transform (CHT). The outlines of the corresponding exact solutions are presented graphically. As far as the information currently available, the derived solutions in this exploration are all new and are expected to enable us to investigate the dynamic characteristics of the considered equation better.

Multi-soliton solutions and soliton molecules of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for the incompressible fluid

The (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) is explored in this letter. The multi-soliton solutions (MSSs) are probed via the Hirota bilinear form which is extracted by taking advantage of the Cole-Hopf transform. The soliton molecules (SMs) on the different planes such as the (x,y)-, (x,t)- and (y,t)-planes are investigated via assigning the velocity resonance mechanisms. The dynamic characteristics of the results are unveiled graphically to show the corresponding physical behaviors.

Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach

This manuscript addresses the rational solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation, emphasizing key aspects in response to specific questions. The study begins by elucidating the problem’s significance, highlighting the pursuit of rational solutions for the mentioned equation. The methodology involves obtaining the Hirota bilinear (HB) form through a transformative process. Furthermore, the analysis extends to the dimensionally reduced BLMP equation, specifically exploring lump and rogue wave-like (Rwl) solutions, along with the interaction between kink and lump solutions. The HB forms play a crucial role in this examination. Importantly, the solutions presented in this study are characterized as non-singular and localized. Visualizations of these solutions are instrumental in understanding the equation’s behavior, particularly how the solutions evolve under varying physical conditions. The outcomes are visually conveyed through 3D and surface graphs, offering a comprehensive representation for specific parameter values. In conclusion, this work contributes novel insights beyond previous efforts in the literature, showcasing the importance and advancements in the study of the (3+1)-dimensional BLMP equation.

Analyzing multi-peak and lump solutions of the variable-coefficient Boiti–Leon–Manna–Pempinelli equation: a comparative study of the Lie classical method and unified method with applications

Analyzing multi-peak and lump solutions of the variable-coefficient Boiti–Leon–Manna–Pempinelli equation: a comparative study of the Lie classical method and unified method with applications

Lump solution and interaction solutions to the fourth-order extended (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

In this paper, we explore the exact solutions to the fourth-order extended (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Based on Hirota bilinear method, lump solution, periodic cross-kink solutions and bright-dark soliton solutions were investigated. By calculating and solving, the peak and trough of lump solution are obtained, and the maximum and minimum points of each are solved. The three-dimensional plots and density plots of periodic cross-kink solution and bright-dark soliton solution are drawn and the dynamics of solutions under different parameters are observed.

Lie analysis and nonlinear propagating waves of the (3 + 1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

The (3+1)-dimensional generalized Boiti-Leon-Manna-Pempinelli equation, which describes the evolution of Riemann wave propagation in an in-compressible fluid along three mutually perpendicular axes, is investigated in this research article. The study encompasses the analysis of Lie symmetries, corresponding symmetry reductions, and conservation laws associated with the equation. The Lie symmetry method is employed to determine the infinitesimal generators of the considered equation. Furthermore, commutator table is generated, and symmetry groups corresponding to each infinitesimal generator are derived. By utilizing the similarity reduction technique, the original nonlinear partial differential equation is transformed into nonlinear ordinary differential equations. Then, generalized exp(−ϕ(ζ)) expansion technique is utilized to solve the reduced equations and estimate specific traveling wave solutions for the equation. Moreover, graphical representations are employed to illustrate the traveling wave solutions, employing suitable parameter values. Additionally, the multiplier approach is utilized to calculate conserved vectors for the equation under consideration.

Characteristics of dynamic waves in incompressible fluid regarding nonlinear Boiti-Leon-Manna-Pempinelli model

Distinct models involving nonlinearity are mostly appreciated for illustrating intricate phenomena arise in the nature. The new (3+1)-dimensional generalized nonlinear Boiti-Leon-Manna-Pempinelli (BLMP) model describes the dynamical behaviors of nonlinear waves arise in incompressible fluid. This present effort deals with the well-known governing BLMP equation by adopting two efficient schemes, namely improved tanh and improved auxiliary equation. As a result, a variety of appropriate wave solutions are made available in different type functions. The gathered solutions are figured out to characterize their internal properties for depicting the relevant phenomena. Diverse wave profiles are noticed in 3D, 2D and contour sense after assigning parameter’s values involved in the achieved solutions. The finding results are comparably different and general due to the existing wave solutions. The employed approaches perform in a great way to construct analytic wave solutions of considered evolution equation and deserve further use in relevant research area.

Interaction solutions for the (2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

This paper aims to search for the solutions of the (2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation. Lump solutions, breather solutions, mixed solutions with solitons, and lump-breather solutions can be obtained from the N-soliton solution formula by using the long-wave limit approach and the conjugate complex method. We use both specific circumstances and general higher-order forms of the hybrid solutions as examples. With the help of maple software, we create density and 3D graphs to summarize the dynamic properties of these solutions. Additionally, it is possible to observe how the solutions’ trajectory, velocity, and shape vary over time.

On the Wave Structures to the (3+1)-Dimensional Boiti–Leon–Manna–Pempinelli Equation in Incompressible Fluid

In the present study, two effective methods, the Exp-function method and He’s frequency formulation, are employed to investigate the dynamic behaviors of the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation, which is used widely to describe the incompressible fluid. A variety of the wave structures, including the dark wave, bright-dark wave and periodic wave solutions, are successfully constructed. Compared with the results attained by the methods, the obtained solutions are all new and have not been presented in the other literature. The diverse wave structures of the solutions are presented through numerical results in the form of three-dimensional plots and two-dimensional curves. It reveals that the proposed methods are powerful and straightforward, which are expected to be helpful for the study of travelling-wave theory in fluid.

On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid

We take into account the stochastic Boiti–Leon–Manna–Pempinelli equation (SBLMPE), which is perturbed by a multiplicative Brownian motion. By applying He’s semi-inverse method and the Riccati equation mapping method, we can acquire the solutions of the SBLMPE. Since the Boiti–Leon–Manna–Pempinelli equation is utilized to explain incompressible liquid in fluid mechanics, the acquired solutions may be applied to explain a lot of fascinating physical phenomena. To address how Brownian motion effects the exact solutions of the SBLMPE, we present some 2D and 3D diagrams.

Abundant Solitary Wave Solutions for the Boiti–Leon–Manna–Pempinelli Equation with M-Truncated Derivative

In this work, we consider the Boiti–Leon–Manna–Pempinelli equation with the M-truncated derivative (BLMPE-MTD). Our aim here is to obtain trigonometric, rational and hyperbolic solutions of BLMPE-MTD by employing two diverse methods, namely, He’s semi-inverse method and the extended tanh function method. In addition, we generalize some previous results. As the Boiti–Leon–Manna–Pempinelli equation is a model for an incompressible fluid, the solutions obtained may be utilized to represent a wide variety of fascinating physical phenomena. We construct a large number of 2D and 3D figures to demonstrate the impact of the M-truncated derivative on the exact solution of the BLMPE-MTD.

Obtaining soliton solutions of the nonlinear (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation via two analytical techniques

This paper tackles the recently introduced (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation (4D-BLMPE) utilized to model wave phenomena in incompressible fluid and fluid mechanics. Modified extended tanh expansion method (METEM) and the new Kudryashov scheme are implemented to produce analytical soliton solutions for the presented equation. The traveling wave transformation is constructed, and the homogeneous balance principle is utilized to apply the two proposed techniques. Furthermore, the flat-kink, smooth-kink, singular, and periodic singular solutions are successfully extracted. Some produced solutions are illustrated graphically to understand the physical meaning of the presented model. Moreover, for the first time in this study, the effect of model parameters on kink soliton dynamics is examined, and graphical representations are depicted and interpreted.

The plethora of exact and explicit soliton solutions of the hyperbolic local (4+1)-dimensional BLMP model via GERF method

In this article, some novel results to the hyperbolic local (4+1)-dim Boiti-Leon-Manna-Pempinelli (BLMP) equation signifies the wave propagation over an incompressible fluid. In comparison to deep water, more essential wave capacity conditions are required for the linearization of the wave structure and strong nonlinear aspects are evident in shallow water. The explicit solitary wave solutions of the hyperbolic local (4+1)-dim BLMP equation are secured in this study using the generalized exponential rational function (GERF) approach. The resulting solutions are also validated by the use of computational tools like Maple. The dynamic characteristics of selected obtained solutions are depicted in 3D along their projections and as 2D graphs for various choices of arbitrary parameters. The outcomes demonstrate the effectiveness of the GERF approach for determining the sws of the (4+1)-dim BLMP equation.