Construction of new solutions to the fully nonlinear generalized Camassa-Holm equations by an indirect F function method

An indirect F function method is introduced to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of elliptic equation, this F function is used to map the solutions of the generalized Camassa-Holm equation to those of the elliptic equation. As a result, we can successfully obtain in a unified way and for special values of the parameters of this equation, many exact solutions expressed by various single and combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions (soliton, combined soliton solutions, and triangular solutions) as the modulus m is driven to 1 and 0.

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