By using the theory of bifurcations of dynamical systems to the generalized Kadomtsev-Petviashili equation, the existence of solitary wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient cond
Bifurcations of travelling wave solutions for the generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili equation
✍ Scribed by Yongan Xie; Bowen Zhou; Shengqiang Tang
- Book ID
- 108051872
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 666 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0096-3003
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This paper is concerned with traveling waves for the generalized Kadomtsev}Petviashvili equation (w y)31, t31, i.e. solutions of the form w(t, , y)"u( !ct, y). We study both, solutions periodic in x" !ct and solitary waves, which are decaying in x, and their interrelations. In particular, we prove
a b s t r a c t By using the bifurcation theory of planar dynamical systems to the generalized ZK equations, the existence of smooth and non-smooth travelling wave solutions is proved. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above sol