Abstract
By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin-Bona-Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
Original language | English |
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Pages (from-to) | 1760-1774 |
Number of pages | 15 |
Journal | Applied Mathematics and Computation |
Volume | 175 |
Issue number | 2 |
DOIs | |
State | Published - 15 Apr 2006 |
Keywords
- Bifurcation theory
- Cusp wave
- Generalized Benjamin-Bona-Mahony equation
- Periodic wave
- Smoothness of waves
- Solitary wave