Generalized Kadomtsev Petviashvili Research Articles

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

New exact solutions and related dynamic behaviors of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

New exact solutions and related dynamic behaviors of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

Convergence problem of the generalized Kadomtsev–Petviashvili II equation in anisotropic Sobolev space

Convergence problem of the generalized Kadomtsev–Petviashvili II equation in anisotropic Sobolev space

Wronskian solutions, bilinear Bäcklund transformation, quasi-periodic waves and asymptotic behaviors for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

In this paper, we investigate the integrability of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used in fluid mechanics and theoretical physics. The N-soliton solution is obtained via the Hirota’s bilinear method. The Wronskian solution is derived by using the Wronskian technique for the bilinear form. Through the exchange formula, we deduce the bilinear Bäcklund transformation consisting of four equations and six parameters. In order to consider the quasi-periodic wave having complex structure, one-, two- and three-periodic waves are investigated systemically by combining the Hirota’s bilinear method with Riemann theta function. Furthermore, the corresponding graphs of periodic wave are presented by considering the geometric properties between the characteristic lines. The propagation characteristics of periodic waves are investigated by virtue of the characteristic lines. Finally, the asymptotic relationships between quasi-periodic wave solutions and soliton solutions are established theoretically under a condition of the small amplitude limit. The analytical method used in this paper can be applied in other integrable systems.

Nonlinear dynamics of soliton molecules, hybrid interactions and other wave solutions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation

This work plumbs the nonlinear dynamics of the ([Formula: see text])-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (gKPBe), which is used to describe some interesting physical phenomena in the fields of fluids. The resonance conditions of the soliton molecules on the ([Formula: see text]), ([Formula: see text]) and ([Formula: see text]) planes are investigated and the soliton molecules are obtained on the basis of the N-soliton solutions that are extracted by virtue of the Hirota form. Furthermore, some novel hybrid interactions including the interaction between the soliton and soliton molecule, the interaction between the different soliton molecules are also explored. Finally, the sub-equation approach is exerted to explore the various wave solutions, which include the kinky wave, bright-dark wave and the singular periodic wave solutions. Correspondingly, the graphical descriptions of the attained solutions are drawn to present a better understanding of the physical attributes. The derived solutions can enlarge the exact solutions of the ([Formula: see text])-dimensional gKPBe and lead us to understand the nonlinear dynamic behaviors better.

The positive multi-complexiton solution to a generalized Kadomtsev–Petviashvili equation

Recently, Lin et al. (Appl. Math. Lett. 78 (2018) 112–117) established the resonant multiple-wave solution of a generalized Kadomtsev–Petviashvili (gKP) equation with applications in applied sciences using the linear superposition technique. In the present paper, according to the results obtained by Lin et al. and adopting a systematic method established by Zhou and Manukure, the positive multi-complexiton solution to the generalized Kadomtsev–Petviashvili equation is constructed for the first time. Several simulations in three dimensions are conducted formally in order to examine the dynamic behavior of positive multi-complexiton solutions, particularly the positive single-, double-, and triple-complexion waves. The current research outcomes definitely will enrich studies related to the gKP equation and its exact solutions.

ON THE SEMI-DOMAIN SOLITON SOLUTIONS FOR THE FRACTAL (3+1)-DIMENSIONAL GENERALIZED KADOMTSEV–PETVIASHVILI– BOUSSINESQ EQUATION

The aim of this study is to explore some semi-domain soliton solutions for the fractal (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (GKPBe) within He’s fractal derivative. First, the fractal soliton molecules are plumbed by combining the Hirota equation and fractal two-scale transform. Second, the Bernoulli sub-equation function approach together with the fractal two-scale transform is employed to investigate the other soliton solutions, which include the kink soliton and the rough wave soliton solutions. The impact of the different fractal orders on the physical behaviors of the semi-domain soliton solutions is also discussed graphically. The methods mentioned in this research are expected to provide some new viewpoints on the behaviors of the fractal PDEs.

Bäcklund transformation and interaction solutions of a generalized Kadomtsev–Petviashvili equation with variable coefficients

Kadomtsev–Petviashvili (KP) equation is a classical nonlinear evolution equation applied in many fields such as plasma physics, fluid dynamics and engineering. In general, variable coefficients are of value in reflecting the inhomogeneities of media, nonuniformities of boundaries, and external forces. This paper mainly studies some exact solutions of a generalized KP equation with variable coefficients by using Hirota bilinear method. Based on the bilinear form, one-, two-, N-soliton solution, Bäcklund transformation and Lax pair are obtained. With the use of the test function method, lump solution and interaction solutions of lump-stripe and lump-soliton types are constructed, and the structure of the solutions are shown in three-dimensional figures. The analysis on the interaction solutions reveals new dynamic behaviors and periodic evolutions.

Existence and concentration of nontrivial solitary waves for a generalized Kadomtsev–Petviashvili equation in [formula omitted

In this paper, we study the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with potential in R2 via the variational methods.

Large time behavior and optimal decay estimate for solutions to the generalized Kadomtsev–Petviashvili–Burgers equation in 2D

We consider the Cauchy problem for the generalized Kadomtsev–Petviashvili–Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a spatial anisotropic dissipative term. Under some suitable regularity assumptions on the initial data u0, especially the condition ∂x−1u0∈L1(R2), it is known that the solution to this problem decays at the rate of t−74 in the L∞-sense. In this paper, we investigate the more detailed large time behavior of the solution and construct the approximate formula for the solution at t→∞. Moreover, we obtain a lower bound of the L∞-norm of the solution and prove that the decay rate t−74 of the solution given in the previous work to be optimal.

Optical Solitary Waves and Soliton Solutions of the (3+1)-Dimensional Generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony Equation

Optical Solitary Waves and Soliton Solutions of the (3+1)-Dimensional Generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony Equation

Existence of nontrivial solitary wave for a generalized Kadomtsev–Petviashvili equation with the potential

In this paper, by using the variational methods, we consider the existence of nontrivial solitary wave for a generalized Kadomtsev–Petviashvili equation with a constant potential and a periodic potential in , respectively. In our problem, the nonlinear term f is only continuous, which allows to consider larger classes of nonlinearities than usually assumed.

Nonautonomous lump-periodic and analytical solutions to the ($$\varvec{3+1}$$)-dimensional generalized Kadomtsev–Petviashvili equation

Nonautonomous lump-periodic and analytical solutions to the ($$\varvec{3+1}$$)-dimensional generalized Kadomtsev–Petviashvili equation

New conservation laws of the Boussinesq and generalized Kadomtsev–Petviashvili equations via homotopy operator

According to the tools of linear algebra and calculus of variations, the conservation laws of Boussinesq and generalized Kadomtsev–Petviashvili (gKP) equations are investigated using multipliers and scaling methods. Using the Euler–Lagrange operator, the determining equations are calculated to find the multipliers of Boussinesq equation and the actual density of gKP equation. Then, the flux and density pairs of Boussinesq equation and the corresponding flux of gKP equation are obtained through 2-dimensional homotopy operator.

Classical solutions for the generalized Kadomtsev–Petviashvili I equations

PurposeThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.Design/methodology/approachThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.FindingsThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.Originality/valueThis article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

Anomalous scattering of dark lumps to the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation

The anomalous interactions of dark lumps that are completely different from the general lump collisions of the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation were constructed. Different from the normal interaction mechanisms, lumps with same velocity and depth were obtained by extending the expression of rational solution based on Hirota’s Bilinear method. Moreover, interactions between dark lumps and soliton were also investigated. In particular, rogue wave excited from the lumps and stripe soliton in the interaction duration were observed. The dynamic behavior of dark lumps was analyzed in detail, and the results obtained were illustrated graphically.

A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions

Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This paper aims to extend the classic lower-dimensional integrable models to arbitrary spatial dimension. We investigate the celebrated Kadomtsev–Petviashvili (KP) equation and propose its (n+1)-dimensional integrable extension. Based on the singularity manifold analysis and binary Bell polynomial method, it is found that the (n+1)-dimensional generalized KP equation has N-soliton solutions, and it also possesses the Painlevé property, Lax pair, Bäcklund transformation as well as infinite conservation laws, and thus the (n+1)-dimensional generalized KP equation is proven to be completely integrable. Moreover, various types of localized solutions can be constructed starting from the N-soliton solutions. The abundant interactions including overtaking solitons, head-on solitons, one-order lump, two-order lump, breather, breather-soliton mixed solutions are analyzed by some graphs.

Novel wave behaviors of the generalized Kadomtsev–Petviashvili modified equal width-burgers equation via modified mathematical methods

In this paper, we have employed two different forms of mathematical methods, namely the extended simple equation method, and modified [Formula: see text]-expansion method to establish several types of solutions of the generalized Kadomtsev–Petviashvili modified equal width-Burgers (G-KP-MEW-B) equation that is used to designate the propagation of long-wave with dissipation and dispersion in nonlinear media. A suitable transform is applied to convert into an ordinary differential equation. As a result, after implementation of the proposed schemes, distinct types of solutions are obtained in the form of exponential hyperbolic, trigonometric and rational functions. To analyze the physical phenomena of the model, some constructed solutions are plotted in 2-dimensional and 3-dimensional by inserting the specific values to attached parameters. Hence, the recommended schemes are highly admirably mathematical tools to evaluate the wave solutions of various models in nonlinear science.

Explicit propagating electrostatic potential waves formation and dynamical assessment of generalized Kadomtsev–Petviashvili modified equal width-Burgers model with sensitivity and modulation instability gain spectrum visualization

The major motive of this study is to analyze the nonlinear integrable model which is generalized Kadomtsev–Petviashvili modified equal width-Burgers equation. It can be utilized extensively a weakly non-linear restoring forces, dispersion, small damping and nonlinear media with dissipation to narrate the long wave propagation in chemical theory. This article allocates the partial differential equation by traveling waves transformation into an ordinary differential equation. In order to acquire the analytical propagating structures, one of the generalized techniques, new extended direct algebraic methodology utilizers. As a consequence, we establish the mixed singular solution, singular solution, mixed shock-singular solution, mixed complex solitary-shock solution, mixed periodic results, mixed trigonometric results have been derived in the formation of a mixed periodic and periodic class, the mixed hyperbolic solution, plane solution, which is derived via Mathematica. The Chaos investigation is carried out to envision the dynamical insights of ocean wave integrable model. The sensitive analysis performed to verify the perceptiveness of model regarding parameters and initial conditions. Modulational instability gain spectrum developed and envisaged with appropriate parametric values and ensured the stability of the considered model. In addition, two-dimension, three-dimension, and contour surfaces are embellished to validate the physical properties of the derived solutions. The developed electro potential soliton structures can reveal the deep atomic insights. The dynamics of physical phenomenon can be controlled by fractional parameter.