Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

Abstract

We use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudosphericalsurfaces for the KdV-Burgers-Kuramoto and nonlinear Schr\"{o}dinger equations with constant Gaussian curvature $-1$. Travelling wave solutions for the above equations are obtained by using a sech-tanh method and Wu's elimination method.