The bifurcation and peakons for the special 𝐶(3, 2, 2) equation

Pramana

Lina Zhang1¹ 

[1] Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, People’s Republic of China$$

关键词: 𝐶(3;    2;    2) equation;    peakons;    bell-shaped solitary waves;    periodic cusp waves.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we investigate a special 𝐶(3, 2, 2) equation $$u_t + ku_x − u_{xxt} + 3(u^3)_x = u_x(u^2)_{xx} + u(u^2)_{xxx}$$.The bifurcation and some new exact representations of peakons, bell-shaped solitary wave solutions and periodic cusp wave solutions for the equation are obtained using the qualitative theory of dynamical systems. It is shown that the peakons are actually the limit of bell-shaped solitary waves and periodic cusp waves. Moreover, a new characteristic of non-smooth solutions, two peakons coexisting for the same wave speed, is found. Some previous results are extended.

【 授权许可】

Unknown