Dimensional 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

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

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

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.

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.

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.

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.

Exact Solution of ( 4 + 1 )-Dimensional Boiti–Leon–Manna–Pempinelli Equation

Based on the Hirota bilinear method, using the heuristic function method and mathematical symbolic computation system, various exact solutions of the ( 4 + 1 )-dimensional Boiti–Leon–Manna–Pempinelli equation including the block kink wave solution, block soliton solution, periodic block solution, and new composite solution are obtained. Upon selection of the appropriate parameters, three-dimensional and contour diagrams of the exact solution were generated to illustrate their properties.

Wave interactions and structures of (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Wave interactions and structures of (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Some new kink type solutions for the new (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Exact solutions of higher-dimensional nonlinear equations takes a major place in the study of nonlinear phenomena observed in nature. In this article, some new kink type solutions are investigated for the new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation. Firstly, a variety of solutions are obtained by Hirota’s bilinear form, which include kink type wave solution, periodic solitary wave solutions and singular solitary wave solutions using extended homoclinic test approach. Secondly, solutions with three wave form are obtained by generalized three wave method. The extended homoclinic test approach is also used to construct solutions with a tail which explain some physical phenomenon. Moreover, some figures of the solutions are shown behind.

Traveling wave solutions of [formula omitted]-dimensional Boiti–Leon–Manna–Pempinelli equation by using improved tanh([formula omitted])-expansion method

Aim of this article is to investigate soliton solutions of recently developed 3+1-dimensional Boiti–Leon–Manna–Pempinelli equation by utilizing newly derived approach namely, improved tanh(ϕ2)-expansion method. As a result, we succeed to secure various types of new solutions for this model including kink, periodic rational solutions. Some of the derived solutions has been discussed in the form of 2-,3-dimensional graphs and their contour plots to visualize the wave dynamics graphically. The results generated by this technique proves that it is a straightforward, robust, and effective method to generate variety of solutions and can be applied on different nonlinear models.

Variable separation solution for an extended (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

This paper proposes a new variable separation solution for the (3+1)-dimensional nonlinear evolution equation. The new variable separation solution directly gives the analytical form of the solution u instead of its potential uy and renders a distinct way to construct localized excitation. Taking the extended (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation as an example, we test its integrability at first. Then, we analyze the elastic, inelastic head-on collision of two and three folded solitary waves by introducing several suitable multi-valued functions. Specifically, the superimposed structure of folded waves is studied, and plenty of novel patterns have been obtained.

ABUNDANT EXACT TRAVELING WAVE SOLUTIONS TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL BOITI–LEON–MANNA–PEMPINELLI EQUATION

Based on the local fractional derivative, we develop a new local fractional (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. With the help of the traveling wave transform of the nondifferentiable type, we convert the local fractional equation into a nonlinear local fractional ordinary differential equation (ODE). Then the Mittag-Leffler function-based method is presented here for the first time to construct the abundant nondifferentiable exact traveling wave solutions, and three families (six sets) of the exact solutions are obtained. In addition, the performances of different solutions on the Cantor set are presented via numerical results in the form of 3D plots. It reveals that the proposed method is simple and straightforward, which can be used to study the local fractional partial differential equations (PDEs).

Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

In the paper, we search for some analytical solutions for a new (3 + 1)‐dimension Boiti–Leon–Manna–Pempinelli (BLMP) equation. Based on the Hirota bilinear method, bilinear neural network framework expands to more than one hidden layer to construct test functions. By using the symbolic computation software Maple, periodic‐type I, II, and III solutions of the new (3 + 1)‐dimension BLMP equation are obtained. Besides, the evolution and dynamical characteristics of these solutions derived via the appropriate real values are also exhibited.

Complexiton and resonant multi-solitons of a (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Complexiton and resonant multi-solitons of a (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Exact solutions of the (3+1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

In this paper, we study exact solutions of the (3[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation. We employ the Hirota bilinear method to obtain the multi-solitary wave solutions, soliton resonant solutions, periodic solutions and interactional solutions and periodic resonant solutions. The corresponding asymptotic features and images are also clearly given.

Breather molecules and localized interaction solutions in the (2+1)-dimensional BLMP equation

The (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is an important integrable model. In this paper, we obtain the breather molecule, the breather-soliton molecule and some localized interaction solutions to the BLMP equation. In particular, by employing a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques, we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump, as well as a bell-shaped soliton and lump. Due to the lack of the long wave limit, it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump. The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations.

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation