Periodic wave solutions and asymptotic analysis of the Hirota-Satsuma shallow water wave equation

2014 ◽  
Vol 38 (17) ◽  
pp. 4262-4271 ◽  
Author(s):  
Zhonglong Zhao ◽  
Yufeng Zhang
Keyword(s):  
Wave Equation ◽  
Asymptotic Analysis ◽  
Shallow Water ◽  
Water Wave ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

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.

scholarly journals Diversity of Interaction Solutions of a Shallow Water Wave Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Bo Ren ◽  
Yong-Li Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
General Theory ◽  
Shallow Water ◽  
Water Wave ◽  
Direct Method ◽  
Soliton Solutions ◽  
Interaction Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions, which can be applied to generate many important solutions, such as lumps and lump-soliton solutions. This is an interesting feature of this research. In addition, we prove this new model is integrable in Painlevé sense. Finally, the diversity of interactive wave solutions of the gHSI is graphically displayed by selecting specific parameters. All the obtained results can be applied to the research of fluid dynamics.

More on Bifurcations and Dynamics of Traveling Wave Solutions for a Higher-Order Shallow Water Wave Equation

2019 ◽  
Vol 29 (01) ◽  
pp. 1950014
Author(s):  
Jibin Li ◽  
Guanrong Chen
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Wave Model ◽  
Periodic Wave ◽  
Wave System ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Straight Lines

This paper studies the dynamics of traveling wave solutions to a shallow water wave model with a large-amplitude regime in phase space. The corresponding traveling wave system is a singular planar dynamical system with two singular straight lines. By using the method of dynamical systems, bifurcation diagrams are obtained. The existence of solitary wave solutions, periodic wave solutions, peakon, pseudo-peakon solution, periodic peakon solutions and compacton solutions are determined under different parameter conditions.

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