Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation

doi:10.1088/1674-1056/abd7d1

中国物理B ›› 2021, Vol. 30 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/abd7d1

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Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation

Bin He(何斌) and Qing Meng(蒙清)^†

College of Mathematics and Statistics, Honghe University, Mengzi 661100, China

收稿日期:2020-11-19 修回日期:2020-12-28 接受日期:2021-01-04 出版日期:2021-05-18 发布日期:2021-05-18
通讯作者: Qing Meng E-mail:mengqhhu@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11461022).

Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation

Bin He(何斌) and Qing Meng(蒙清)^†

College of Mathematics and Statistics, Honghe University, Mengzi 661100, China

Received:2020-11-19 Revised:2020-12-28 Accepted:2021-01-04 Online:2021-05-18 Published:2021-05-18
Contact: Qing Meng E-mail:mengqhhu@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11461022).

摘要/Abstract

摘要： The Schamel-Korteweg-de Vries equation is investigated by the approach of dynamics. The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses. The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given. All possible exact explicit parametric representations of the waves are also presented. Along with the details of the analyses, the analytical results are numerically simulated lastly.

关键词: Schamel-Korteweg-de Vries equation, dynamical behavior, solitary wave solution, periodic wave solution

Abstract: The Schamel-Korteweg-de Vries equation is investigated by the approach of dynamics. The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses. The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given. All possible exact explicit parametric representations of the waves are also presented. Along with the details of the analyses, the analytical results are numerically simulated lastly.

Key words: Schamel-Korteweg-de Vries equation, dynamical behavior, solitary wave solution, periodic wave solution

中图分类号: (Ordinary differential equations)

02.30.Hq

02.30.Oz (Bifurcation theory) 04.20.Jb (Exact solutions)

Bin He(何斌) and Qing Meng(蒙清). Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation[J]. 中国物理B, 2021, 30(6): 60201-060201.

Bin He(何斌) and Qing Meng(蒙清). Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation[J]. Chin. Phys. B, 2021, 30(6): 60201-060201.

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Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation

Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation

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