Classification of the Travelling Wave Solutions of the Sharma–Tasso–Olver Equation

The Sharma–Tasso–Olver (STO) equation is an integrable nonlinear partial differential equation that arises in various physical contexts, including fluid dynamics, plasma physics, and nonlinear optics. In this work, a complete analytical treatment of the travelling wave solutions of the STO equation is provided. The analysis reveals a family of exact solutions broader than those found in the literature.