Dimensional Kadomtsev-Petviashvili Research Articles

Complexiton, complex multiple kink soliton and the rational wave solutions to the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation

Abstract Some new exact solutions of the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation (KPE) are explored in this study. Firstly, the resonant multiple soltion solutions (RMSs) are discussed via employing the linear superposition principle and weight algorithm. Then, by introducing pairs of the conjugate parameters to the RMSs, the complexiton solutions including the non-singular complexiton and singular complexiton solutions are extracted. In addition, the complex multiple kink soliton solutions are also probed by employing the bilinear approach. Finally, we investigate the rational wave solutions via the test function method and symbolic computation. By choosing the appropriate parameters, the graph descriptions of the derived solutions are presented to show the dynamical properties. The outcomes of this work are desirous to bring some new perspective to the study of the complexiton, complex solutions and rational wave solutions to the other PDEs.

VARIATIONAL PERSPECTIVE TO (2+1)-DIMENSIONAL KADOMTSEV–PETVIASHVILI MODEL AND ITS FRACTAL MODEL

In this work, the [Formula: see text]-dimensional Kadomtsev–Petviashvili model is investigated. A novel variational scheme, namely, the variational transform wave method (VTWM), is successfully established to seek the solitary wave solution of the Kadomtsev–Petviashvili model. Furthermore, the fractal solitary solution of fractal Kadomtsev–Petviashvili model is also studied based on the local fractional derivative. Numerical examples are given to fully demonstrate that the VTWM is straightforward, efficient and attractive. Finally, the physical properties of solitary wave solutions are demonstrated by some 3D graphs.

Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a ($$3+1$$)-dimensional Kadomtsev–Petviashvili equation

Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a ($$3+1$$)-dimensional Kadomtsev–Petviashvili equation

Bilinear Bäcklund Transformation, Fission/Fusion and Periodic Waves of a (3+1)-dimensional Kadomtsev-Petviashvili Equation for the Shallow Water Waves

Bilinear Bäcklund Transformation, Fission/Fusion and Periodic Waves of a (3+1)-dimensional Kadomtsev-Petviashvili Equation for the Shallow Water Waves

Multiple soliton, soliton molecules and the other diverse wave solutions to the (2+1)-dimensional Kadomtsev–Petviashvili equation

The central purpose of this paper is to explore the nonlinear dynamics of the (2+1)-dimensional Kadomtsev–Petviashvili equation (KPE). The multiple soliton solutions (MSSs) are constructed via applying the Hirota method. Then the soliton molecules on the ([Formula: see text]-, ([Formula: see text]- and ([Formula: see text]-planes are extracted via imposing the velocity resonance conditions to the MSSs. Eventually, two effective techniques, the sub-equation approach (SEA) and the variational approach (VA), are employed to probe some other diverse wave solutions, which are the bright wave, dark wave, singular wave and the singular periodic wave solutions. The dynamics of the extracted solutions are unveiled graphically to exhibit the physical attributes. The attained solutions in this paper can enlarge the exact solutions of the (2+1)-dimensional KPE and enable us to understand the nonlinear dynamic behaviors better.

Breather waves, periodic cross-lump waves and complexiton type solutions for the (2 + 1)-dimensional Kadomtsev-Petviashvili equation in dispersive media

The manuscript under consideration explores the (2+1)-dimensional Kadomtsev-Petviashvili (KP) model using its bilinear representation. The focus is on studying the characteristics of periodic cross-lump waves and breather wave solutions. Breathers, which are localized periodic solutions of continuous media equations or discrete lattice equations, are of particular interest. The research also delves into complexiton solutions using the extended transformed rational function approach. The study graphically analyzes the dynamics of these interaction solutions using appropriate parameters. It's truly fascinating to learn about the application of breathers in continuous media equations or discrete lattice equations.

Exact solutions of the time-fractional extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Exact solutions of the time-fractional extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Interactions of certain localized waves for an extended (3+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics

Currently, there is much interest in the study on the localized waves and their interactions in fluid mechanics. An extended (3+1)-dimensional Kadomtsev-Petviashvili equation is considered here. By means of the Hirota method, we obtain the N-soliton solutions, with N as a positive integer. The higher-order breather solutions are obtained from the N-soliton solutions through the complex conjugated transformations. Making use of the long-wave limit method, we determine the higher-order lump solutions via the N-soliton solutions. Besides, some hybrid solutions are presented. Three kinds of the localized waves, namely, the solitons, breathers and lumps, along with their interactions, are investigated via the above solutions. Amplitudes, shapes and velocities of those localized waves remain invariant after the interactions, which indicate that the interactions are elastic. Fluid-mechanically meaningful, all our results rely on the coefficients in that equation.

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

This article presents an investigation for soliton solutions of the extended (2+1)-dimensional Kadomtsev–Petviashvili equation which describes wave behavior in shallow water. We utilize the unified Riccati equation expansion method. By employing the powerful method, many soliton solutions are successfully derived, and it is verified by Wolfram Mathematica that the solutions satisfy the main equation. Additionally, Matlab is utilized to generate plots and examine the properties of the obtained solitons. The results reveal that the considered equation exhibits a wide range of soliton solutions, including dark, bright, singular, and periodic solutions. This comprehensive investigation of soliton solutions for the Kadomtsev–Petviashvili equation holds significant relevance in various fields such as oceanography and nonlinear optics, contributing to practical applications.

New analytic wave solutions to (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation using the modified extended mapping method

New analytic wave solutions to (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation using the modified extended mapping method

Analytical and numerical simulation of the conformable new extended (2 + 1) dimensional Kadomtsev–Petviashvili equation

Partial differential equations are used to model problems in many scientific fields. To solve these equations, analytical and numerical techniques are created. This study considers the conformable version of the expanded Kadomtsev–Petviashvili equation in -dimensions for the first time. New exact and approximative solutions to the equation that do not exist in the literature are obtained using the analytical techniques of the -expansion and modified Kudryashov methods, as well as the numerical technique residual power series method. To better understand the dynamic nature of these findings, we have given 3D, contour, and 2D plots of some of the solutions. The development of numerous new exact solutions has demonstrated the reliability and effectiveness of the methods. We also provide an approximation table of values for the approximate solutions of the given equation using different values for various parameters.

Soliton Solutions to the BA Model and (3 + 1)-Dimensional KP Equation Using Advanced exp − ϕ ξ -Expansion Scheme in Mathematical Physics

In this manuscript, the primary motivation is the implementation of the advanced exp − ϕ ξ -expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Here, the solutions’ behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced exp − ϕ ξ -expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced exp − ϕ ξ -expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences.

Traveling Wave Solutions and Bifurcations of a New Generalized (3 + 1)-Dimensional Kadomtsev–Petviashvili Equation

Traveling Wave Solutions and Bifurcations of a New Generalized (3 + 1)-Dimensional Kadomtsev–Petviashvili Equation

Symmetry and complexity: A Lie symmetry approach to bifurcation, chaos, stability and travelling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation

This work delves into the investigation of the nonlinear dynamics pertaining to the (3+1)-dimensional Kadomtsev-Petviashvili equation, which describes the propagation of long-wave with dissipation and dispersion in nonlinear media. The research entails an exploration of symmetry reductions using Lie group analysis, an analysis of the dynamical system’s characteristics through bifurcation phase portraits, and a study of the perturbed dynamical system’s dynamic behavior through chaos theory. Chaotic behavior is identified using various tools for detecting chaos, including the Lyapunov exponent, 3D phase portrait, Poincare map, time series analysis, and an exploration of the presence of multistability in the autonomous system under different initial conditions. Additionally, the research applies the unified Riccati equation expansion method to solve the considered equation analytically and constructs the general solutions of solitary wave solutions such as trigonometric function solutions, periodic and singular soliton solutions. These solutions come with their associated constraint conditions and are demonstrated through visual representations in the form of 2D, 3D, and density plots with carefully selected parameters. Furthermore, the stability analysis of the considered equation is also discussed and shown graphically. The results of this work are relevant and have applications in describing the propagation of long-wave with dissipation and dispersion in nonlinear media.

Periodic, n-soliton and variable separation solutions for an extended (3+1)-dimensional KP-Boussinesq equation

An extended (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation is studied in this paper to construct periodic solution, n-soliton solution and folded localized excitation. Firstly, with the help of the Hirota’s bilinear method and ansatz, some periodic solutions have been derived. Secondly, taking Burgers equation as an auxiliary function, we have obtained n-soliton solution and n-shock wave. Lastly, we present a new variable separation method for (3+1)-dimensional and higher dimensional models, and use it to derive localized excitation solutions. To be specific, we have constructed various novel structures and discussed the interaction dynamics of folded solitary waves. Compared with the other methods, the variable separation solutions obtained in this paper not only directly give the analytical form of the solution u instead of its potential u_y, but also provide us a straightforward approach to construct localized excitation for higher order dimensional nonlinear partial differential equation.

A Generalized (3+1)-Dimensional Nonlinear Wave Equation in Liquid with Gas Bubbles: Symmetry Reductions; Exact Solutions; Conservation Laws

The analysis of a generalised (3+1)-dimensional nonlinear wave equation that simulates a variety of nonlinear processes that occur in liquids including gas bubbles will be performed. After some cosmetic adjustments to the underlying equation, this generalised (3+1)-dimensional nonlinear wave equation naturally degenerates into the (3+1)-dimensional Kadomtsev-Petviashvili equation, the (3+1)-dimensional nonlinear wave equation, and the Korteweg-de Vries equation. To completely investigate this fundamental equation, a clear and rigorous technique is used. In order to obtain innovative symmetry reductions, group invariant solutions, conservation laws, and eventually kink wave solutions, the Lie symmetry, multiplier, and simplest equation methods are used. Complex waves and their dealing dynamics in fluids can be well imitated by the verdicts.

Analytical solutions of the extended Kadomtsev–Petviashvili equation in nonlinear media

Abstract This manuscript attempts to construct diverse exact traveling wave solutions for an important model called the (3+1)-dimensional Kadomtsev–Petviashvili equation. In order to achieve that, the Jacobi elliptic function technique and the Kudryashov technique are chosen in favor of their noticeable efficacy in dealing with nonlinear dynamical models. As expected, the used approaches lead to a variety of traveling wave solutions of different types. Finally, we have graphically illustrated some of the obtained wave solutions to further make sense of their representation. Also, we provide an overview of the main results at the end.

(3+1)-dimensional cylindrical dust ion-acoustic solitary waves in dusty plasma

The basic properties of (3+1)-dimensional cylindrical dust ion-acoustic (DIA) solitary waves have been studied in a multi-component plasma medium consisting of inertial ions, Maxwellian electrons, and stationary negative dust particles. The reductive perturbation method has been used to derive a cylindrical (3+1)-dimensional Kadomtsev–Petviashvili equation for small but finite amplitude of dust ion-acoustic waves. The impacts of nonplanar geometry and presence of static negative dust particles on the dust ion-acoustic solitary structures have been investigated. DIA solitary waves with both positive and negative polarity is observed to generate for this existing multi-component and complex plasma medium. The changes in the DIA wave structure in radial, azimuthal, and axial coordinates over time have been presented analytically. The results of this present investigation may contribute to a better understanding of laboratory plasma events as well as nonlinear electrostatic excitations in astrophysical environments.

Dynamics of nonlinear dark waves and multi-dark wave interactions for a new extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Dynamics of nonlinear dark waves and multi-dark wave interactions for a new extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Novel investigations of dual-wave solutions to the Kadomtsev–Petviashvili model involving second-order temporal and spatial–temporal dispersion terms

Our work presents a novel insight into a higher dimensional Kadomtsev–Petviashvili (KP) model, wherein we observe that the propagation of the proposed model is characterized by the movement of symmetric dual waves. These waves are the result of the superposition of two waves with equal amplitude and opposite phase, which arises due to the involvement of a second-order temporal dispersion term in the model. Our study involves several schemes, leading to the discovery of various physical structures associated with the KP model. In summary, our research emphasizes that the simultaneous propagation of symmetric waves has significant practical applications in numerous fields where precise measurement, control, or analysis of waves is crucial.