| Volume 10, Number 1, 2020, Pages 267-281 DOI：10.11948/20190140 |
| Traveling Waves of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation |
| Lan Wang,Yuqian Zhou,Qian Liu,Qiuyan Zhang |
| Keywords:KP-Boussinesq equation, traveling waves, bifurcation, dynamical system. |
| Abstract: |
| In this paper, the bifurcation theory of dynamical system is applied to study the traveling waves of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq (KP-Boussinesq) equation. By transforming the traveling wave system of the KP-Boussinesq equation into a dynamical system in $R^{3}$, we derive various parameter conditions which guarantee the existence of its bounded and unbounded orbits. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all possible traveling wave solutions of the (3+1)-dimensional KP-Boussines equation. |
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