Application of the division theorem to nonlinear physical models for constructing traveling waves

Abstract

We extend the so-called first integral method, which is based on the division theorem, to the Sharma-Tasso-Olver equation and the (2+1)-dimensional modified Boussinesq equation. Our approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Traveling wave solutions are constructed through the established first integrals.