Search results for "Dark solitons"

Global dynamical behaviors in a physical shallow water system

2016

International audience; The theory of bifurcations of dynamical systems is used to investigate the behavior of travelling wave solutions in an entire family of shallow water wave equations. This family is obtained by a perturbative asymptotic expansion for unidirectional shallow water waves. According to the parameters of the system, this family can lead to different sets of known equations such as Camassa-Holm, Korteweg-de Vries, Degasperis and Procesi and several other dispersive equations of the third order. Looking for possible travelling wave solutions, we show that different phase orbits in some regions of parametric planes are similar to those obtained with the model of the pressure …