scholarly journals TRAVELING WAVE, LUMP WAVE, ROGUE WAVE, MULTI-KINK SOLITARY WAVE AND INTERACTION SOLUTIONS IN A (3+1)-DIMENSIONAL KADOMTSEVPETVIASHVILI EQUATION WITH BÄCKLUND TRANSFORMATION

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Shou-Fu Tian ◽  
◽  
Ding Guo ◽  
Xiu-Bin Wang ◽  
Tian-Tian Zhang
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Rogue Wave ◽  
Interaction Solutions ◽  
Cklund Transformation ◽  
Lump Wave

scholarly journals Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel’nikov System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yue-jun Deng ◽  
Rui-yu Jia ◽  
Ji Lin
Keyword(s):  
Rational Function ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Bright Soliton ◽  
Half Line ◽  
Exponential Functions ◽  
Interaction Solutions ◽  
Mixed Solutions ◽  
Lump Wave ◽  
Interaction Phenomena

Lump wave and line rogue wave of the (2 + 1)-dimensional Mel’nikov system are derived by taking the ansatz as the rational function. By combining a rational function and different exponential functions, mixed solutions between the lump and soliton are derived. These solutions describe the interaction phenomena of the lump-bright soliton with fission and fusion, the half-line rogue wave with a bright soliton, and a rogue wave excited from the bright soliton pair, respectively. Some special concrete interaction solutions are depicted in both 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.

Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Jiyu Zhong ◽  
Shengfu Deng
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Planar Systems

In this paper, we investigate the traveling wave solutions of a two-component Dullin–Gottwald–Holm (DGH) system. By qualitative analysis methods of planar systems, we investigate completely the topological behavior of the solutions of the traveling wave system, which is derived from the two-component Dullin–Gottwald–Holm system, and show the corresponding phase portraits. We prove the topological types of degenerate equilibria by the technique of desingularization. According to the dynamical behaviors of the solutions, we give all the bounded exact traveling wave solutions of the system, including solitary wave solutions, periodic wave solutions, cusp solitary wave solutions, periodic cusp wave solutions, compactonlike wave solutions, and kinklike and antikinklike wave solutions. Furthermore, to verify the correctness of our results, we simulate these bounded wave solutions using the software maple version 18.

Localized interaction solution and its dynamics of the extended Hirota–Satsuma–Ito equation

2021 ◽  
pp. 2150313
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Chaudry Masood Khalique ◽  
Yong-Li Sun
Keyword(s):  
Numerical Simulations ◽  
Rogue Wave ◽  
The Other ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Physical Phenomena ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Ito Equation

In this research, we will introduce and study the localized interaction solutions and th eir dynamics of the extended Hirota–Satsuma–Ito equation (HSIe), which plays a key role in studying certain complex physical phenomena. By using the Hirota bilinear method, the lump-type solutions will be firstly constructed, which are almost rationally localized in all spatial directions. Then, three kinds of localized interaction solutions will be obtained, respectively. In order to study the dynamic behaviors, numerical simulations are performed. Two interesting physical phenomena are found: one is the fission and fusion phenomena happening during the procedure of their collisions; the other is the rogue wave phenomena triggered by the interaction between a lump-type wave and a soliton wave.

Pseudo-Peakon, Periodic Peakons and Compactons on a Shallow Water Model with Coriolis Effect

2021 ◽  
Vol 31 (08) ◽  
pp. 2150144
Author(s):  
Zhenshu Wen ◽  
Guanrong Chen ◽  
Jibin Li
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Solitary Wave Solution ◽  
Wave Theory ◽  
Water Model ◽  
Wave System ◽  
Coriolis Effect ◽  
Bounded Solutions ◽  
Shallow Water Model

For a shallow water model with Coriolis effect, by applying the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to its traveling wave system, under different parameter conditions, all possible bounded solutions (solitary wave solution, pseudo-peakon and periodic peakons as well as compactons) are obtained. Some exact explicit parametric representations are presented.

Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

2020 ◽  
Vol 30 (03) ◽  
pp. 2050036 ◽  
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Two Component ◽  
Wave Models

For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

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