Dynamics and Bifurcations of Travelling Wave Solutions of 𝑅(𝑚, 𝑛) Equations

Proceedings Mathematical Sciences

Dahe Feng²  Jibin Li¹ 

[1] Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 00, People’s Republic of China$$;School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 00, People’s Republic of China$$

关键词: 𝑅(𝑚;    𝑛) equations;    solitary wave;    periodic wave;    breaking wave;    solitary cusp wave;    periodic cusp wave.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

By using the bifurcation theory and methods of planar dynamical systems to 𝑅(𝑚, 𝑛) equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave, smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling wave solutions are listed.

【 授权许可】

Unknown