Applications of Backlund Transformations to Explicit and Exact Solutions in Nonlinear Wave Equations

摘要

Backlund transformations and heat equation are used to find several families of explicit and exact solutions for the well-known Whitham-Broer-Kaup equations in shallow water and Kupershmidt equations. In result, multi-soliton solutions, rational fraction solutions and soliton-like solutions are obtained.