Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal

Abstract EN

We investigate the traveling solitary wave solutions of the generalized Camassa-Holm equation u t - u x x t + 3 u 2 u x = 2 u x u x x + u u x x x on the nonzero constant pedestal lim ξ → ± ∞ u ξ = A .

Our procedure shows that the generalized Camassa-Holm equation with nonzero constant boundary has cusped and smooth soliton solutions.

Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa-Holm equation.

Some exact explicit solutions are obtained.

We show some graphs to explain our these solutions.