Hamiltonian Structure, Soliton Solution and Conservation Laws for a New Fifth-Order Nonlinear Evolution Equation Which Describes Pseudo-Spherical Surfaces

Abstract

In this paper, we shall show that the Hamiltonian structure can be defined for any nonlinear evolution equations which describe surfaces of a constant negative curvature, so that the densities of conservation laws can be considered as corresponding Hamiltonians. This paper obtains the soliton solution and conserved quantities of a new fifth-order nonlinear evolution equation by the aid of inverse scattering method.

Exact Solitary Wave Solutions for the Generalized Schamel Korteweg–De Vries Equation

“…In this paper, we use the sine-cosine method to study the generalized S-KdV equation. This method provides the soliton-like solutions, the kink solutions, and plural solutions (Sayed & Al-Atawi, 2017). The presented exact solutions can describe various new features of waves and then may be useful in the theoretical and numerical studies of the considered equation.…”