Solitary wave solutions, fusionable wave solutions, periodic wave solutions and interactional solutions of the (3+1)-dimensional generalized shallow water wave equation

2021 ◽  
pp. 2150389
Author(s):  
Ai-Juan Zhou ◽  
Bing-Jie He
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this paper, we study exact solutions of the generalized shallow water wave equation. Based on the bilinear equation, we get [Formula: see text]-solitary wave solutions. For special parameters, we find [Formula: see text]-fusionable wave solutions. For complex parameters, periodic wave solutions and elastic interactional solutions of solitary waves with periodic waves are obtained. The properties of obtained exact solutions are also analyzed theoretically and graphically by using asymptotic analysis.

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

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].

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