Generalized transformations and abundant new families of exact solutions for (2 + 1)-dimensional dispersive long wave equations

Abstract

A new generalized transformation based upon the well-known Riccati equation is presented and applied to find exact solutions of the (2 + 1)-dimensional dispersive long wave equation. Many explicit exact solutions are obtained that include new solitary and periodic wave solutions, and combined formal solitary and periodic wave solutions. The variant Boussinesq equation, as a special case of the (2 + 1)-dimensional dispersive long wave equation, is also solved. These exact solutions are obtained computationally using the Wu elimination method with the aid of Mathematica to solve the large system of algebraic equations produced by the solution ansatz.