New explicit periodic wave solutions and their limits for modified form of Camassa-Holm equation
This paper is devoted to the study of the following nonlinear equation \[ u_t+2ku_x-u_{xxt}+au^2u_x=2u_xu_{xx}+uu_{xxx}, \] which is a modified form of the Camassa-Holm equation. Using the bifurcation method of dynamical systems, some new explicit periodic wave solutions in terms of Jacobian elliptic functions are constructed. The authors also obtain some explicit solitary wave solutions in terms of hyperbolic functions via the limits of the explicit periodic wave solutions.
scientific article; zbMATH DE number 5788812
scientific article