Degeneration of solitons for a ($$3+1$$)-dimensional generalized nonlinear evolution equation for shallow water waves

Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

Special Session 31: Nonlinear Waves and Solitons

The strongly coupled nonlinear Schr odinger equations are studied numerically to gain insight into an increasingly complex family of collision interactions. Speci cally, the case of apparent repulsion between soliton solutions are considered in terms of phase velocity, relative shift, and apparent trajectory. Both elastic and inelastic collisions are discussed. −→∞ ∞←− anisotropic e ects on por...

Exact Solutions of the Nonlinear Generalized Shallow Water Wave Equation

Submitted: Nov 12, 2013; Accepted: Dec 18, 2013; Published: Dec 22, 2013 Abstract: In this article, we have employed an enhanced (G′/G)-expansion method to find the exact solutions first and then the solitary wave solutions of the nonlinear generalized shallow water wave equation. Here we have derived solitons, singular solitons and periodic wave solutions through the enhanced (G′/G)-expansion ...

Evolution of solitary waves for a perturbed nonlinear Schrödinger equation

Soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear Schrödinger equation. Perturbation terms, which model wide classes of physically relevant perturbations, are considered. An analytical solution is found for the first-order correction of the evolving solitary wave. This solution for the solitary wave tail is in integral form and ...

Nonlinear edge waves and shallow-water theory