Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation

2017 ◽  
Vol 72 (10) ◽  
pp. 955-961 ◽  
Author(s):  
Iftikhar Ahmed
Keyword(s):  
Nonlinear Phenomena ◽  
Kp Equation ◽  
The Third ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Kink Wave ◽  
Kink Waves ◽  
Line Soliton ◽  
Interaction Phenomena

AbstractIn this work, we investigate dimensionally reduced generalised Kadomtsev-Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. Based on the bilinear formalism, direct Maple symbolic computations are used with an ansätz function to construct three classes of interaction solutions between lump and line solitons. Furthermore, the dynamics of interaction phenomena is explained with 3D plots and 2D contour plots. For the first class of interaction solutions, lump appeared at t=0, and there was a normal interaction between lump and line solitons at t=1, 2, 5, and 10. For the second class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving downward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. By contrast, for the third class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving upward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. Furthermore, interaction solutions between lump solutions and kink wave are also investigated. These results might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.

Abundant Lump Solution and Interaction Phenomenon of (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

2019 ◽  
Vol 20 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Jianqing Lü ◽  
Sudao Bilige ◽  
Xiaoqing Gao
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Lump Solution ◽  
Lump Solutions ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Special Case ◽  
Interaction Phenomenon

AbstractIn this paper, with the help of symbolic computation system Mathematica, six kinds of lump solutions and two classes of interaction solutions are discussed to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation via using generalized bilinear form with a dependent variable transformation. Particularly, one special case are plotted as illustrative examples, and some contour plots with different determinant values are presented. Simultaneously, we studied the trajectory of the interaction solution.

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wenying Cui ◽  
Yinping Liu ◽  
Zhibin Li
Keyword(s):  
Fluid Dynamics ◽  
Algebraic Method ◽  
Higher Order ◽  
Decomposition Algorithm ◽  
Periodic Waves ◽  
Order Interaction ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation ◽  
Interaction Phenomena

Abstract In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N-soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

Characteristics of the breather waves, rogue waves and solitary waves in an extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation

2019 ◽  
Vol 29 (8) ◽  
pp. 2964-2976
Author(s):  
Hui Wang ◽  
Shou-Fu Tian ◽  
Yi Chen
Keyword(s):  
Solitary Waves ◽  
Dynamical Behavior ◽  
Rogue Waves ◽  
Graphical Analysis ◽  
Nonlinear Phenomena ◽  
Kp Equation ◽  
Bilinear Method ◽  
Test Technique ◽  
Content Type ◽  
Petviashvili Equation

Purpose The purpose of this paper is to study the breather waves, rogue waves and solitary waves of an extended (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation, which can be used to depict many nonlinear phenomena in fluid dynamics and plasma physics. Design/methodology/approach The authors apply the Bell’s polynomial approach, the homoclinic test technique and Hirota’s bilinear method to find the breather waves, rogue waves and solitary waves of the extended (3 + 1)-dimensional KP equation. Findings The results imply that the extended (3 + 1)-dimensional KP equation has breather wave, rogue wave and solitary wave solutions. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior. Originality/value These results may help us to further study the local structure and the interaction of solutions in KP-type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of such equations.

scholarly journals Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Chuanjian Wang ◽  
Hui Fang
Keyword(s):  
Wave Solution ◽  
Solitary Wave Solutions ◽  
Kink Wave Solution ◽  
Type Wave ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Kink Wave ◽  
Hermitian Quadratic Form

Lump-type wave solution of the Bogoyavlenskii–Kadomtsev–Petviashvili equation is constructed by using the bilinear structure and Hermitian quadratic form. The dynamical behaviors of lump-type wave solution are investigated and presented analytically and graphically. Furthermore, we discuss the interaction between a lump-type wave and a kink wave solution. Absorb-emit interaction between two kinds of solitary wave solutions is shown. This kind of interaction solution can be regarded as a lump-type wave which propagates on the kink wave background.

Lump and interaction solutions of nonlinear partial differential equations

2019 ◽  
Vol 33 (11) ◽  
pp. 1950133 ◽  
Author(s):  
Yong-Li Sun ◽  
Wen-Xiu Ma ◽  
Jian-Ping Yu ◽  
Bo Ren ◽  
Chaudry Masood Khaliqu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Partial Differential ◽  
Interaction Solutions ◽  
Kink Waves ◽  
Hirota Bilinear

In this paper, lump solutions of nonlinear partial differential equations, the generalized (2[Formula: see text]+[Formula: see text]1)-dimensional KP equation and the Jimbo–Miwa equation, are studied by using the Hirota bilinear method and carrying out symbolic computations in Maple. Moreover, the interaction solutions, i.e. collisions between lump waves and kink waves, are investigated. A group of graphs are plotted to illustrate the dynamics of the obtained results.

scholarly journals Lumps, breathers, and interaction solutions of a (3+1)-dimensional generalized Kadovtsev–Petviashvili equation

2020 ◽  
pp. 2150041
Author(s):  
Xi Ma ◽  
Tie-Cheng Xia ◽  
Handong Guo
Keyword(s):  
Soliton Solution ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Test Technique ◽  
Interaction Solutions ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Wave Limit ◽  
Hirota Bilinear

In this paper, we use the Hirota bilinear method to find the [Formula: see text]-soliton solution of a [Formula: see text]-dimensional generalized Kadovtsev–Petviashvili (KP) equation. Then, we obtain the [Formula: see text]-order breathers of the equation, and combine the long-wave limit method to give the [Formula: see text]-order lumps. Resorting to the extended homoclinic test technique, we obtain the breather-kink solutions for the equation. Last, the interaction solution composed of the [Formula: see text]-soliton solution, [Formula: see text]-breathers, and [Formula: see text]-lumps for the [Formula: see text]-dimensional generalized KP equation is constructed.

scholarly journals Abundant lump solutions and interaction solutions of a (3+1)-D Kadomtsev-Petviashvili equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2437-2445 ◽  
Author(s):  
Xiaoqing Gao ◽  
Sudao Bilige ◽  
Jianqing Lü ◽  
Yuexing Bai ◽  
Runfa Zhang ◽  
...  
Keyword(s):  
Lump Solution ◽  
Solution Properties ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Hirota Bilinear

In this paper, abundant lump solutions and two types of interaction solutions of the (3+1)-D Kadomtsev-Petviashvili equation are obtained by the Hirota bilinear method. Some contour plots with different determinant values are sequentially given to show that the corresponding lump solution tends to zero when the deter-minant approaches to zero. The interaction solutions with special parameters are plotted to elucidate the solution properties.

scholarly journals New Periodic Wave, Cross-Kink Wave, Breather, and the Interaction Phenomenon for the (2 + 1)-Dimensional Sharmo–Tasso–Olver Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Hongcai Ma ◽  
Caoyin Zhang ◽  
Aiping Deng
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Periodic Wave ◽  
Periodic Waves ◽  
Trilinear Form ◽  
Interaction Solutions ◽  
Kink Wave ◽  
Kink Waves ◽  
Kink Soliton ◽  
Interaction Phenomenon

In this paper, with the aid of symbolic computation, several kinds of exact solutions including periodic waves, cross-kink waves, and breather are proposed by using a trilinear form for the (2 + 1)-dimensional Sharmo–Tasso–Olver equation. Then, by combing the different forms, the interactions between a lump and one-kink soliton and between a lump and periodic waves are generated. Moreover, the dynamic characteristics of interaction solutions are analyzed graphically by selecting suitable parameters with the help of Maple.

Interaction Behaviours Between Soliton and Cnoidal Periodic Waves for the Cubic Generalised Kadomtsev–Petviashvili Equation

2015 ◽  
Vol 70 (7) ◽  
pp. 539-544 ◽  
Author(s):  
Bo Ren ◽  
Ji Lin
Keyword(s):  
Elliptic Integral ◽  
Elliptic Functions ◽  
Jacobi Elliptic Functions ◽  
Periodic Waves ◽  
The Third ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Kink Soliton

AbstractThe consistent tanh expansion (CTE) method is applied to the cubic generalised Kadomtsev–Petviashvili (CGKP) equation. The interaction solutions between one kink soliton and the cnoidal periodic waves are explicitly given. Some special concrete interaction solutions in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral are discussed both in analytical and graphical ways.

Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Na Yuan ◽  
Jian-Guo Liu ◽  
Aly R. Seadawy ◽  
Mostafa M. A. Khater
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Variable Coefficient ◽  
Periodic Wave ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Self Consistent ◽  
Contour Plots ◽  
Lump Wave ◽  
Interaction Phenomenon

Abstract Under investigation is a generalized variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources. Our main job is divided into four parts: (i) lump wave solution, (ii) interaction solutions between lump and solitary wave, (iii) breather wave solution and (iv) interaction solutions between lump and periodic wave. Furthermore, the interaction phenomenon of waves is shown in some 3D- and contour plots.

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