Abstract
This paper studies the Camassa-Holm equation’s bifurcation solutions by using the local method of Lyapunov-Schmidt. The Camassa-Holm equation has been studied with the formula ODE. We have found the key function corresponding to the functional related to this equation. The bifurcation analysis of this function has been investigated by the boundary singularities. We have found the parametric equation of the bifurcation set (caustic) with the geometric description of this caustic. Also, the critical points’ bifurcation spreading has been found.
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