Bifurcation of travelling wave solutions for the generalized ZK-BBM equations. (English) Zbl 1221.35370
Summary: By using the bifurcation theory of planar dynamical systems to the generalized ZK-BBM 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 solutions are given. Some exact explicit parametric representations of the above waves are determined.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 35Q51 | Soliton equations |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
References:
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