Imperfect bifurcation of Cammasa-Holm equation using

الملخص EN

In this paper, we are studying imperfect bifurcation of the Camassa-Holm equation using the local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the Camassa- Holm equation is given by the nonlinear system of two equations.

The bifurcation diagram of the bifurcation equation showed that there are zero, two or four real solutions.

We considered these solutions as solutions of a dynamical system, then we draw the phase portrait corresponding to the system.