New exact traveling wave solutions of the sharma–tasso–olver equation

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Abstract

This paper introduces a new analytical method for solving the Sharma–Tasso-Olver (STO) equation using the travelling wave technique coupled with the newly established homogeneous balance equation (HBM). The combination of both techniques makes it possible to systematically reduce the nonlinear STO equation to an exactly solvable form. In this paper, three separate cases resulting from the balance condition are examined carefully, and for each case, several sub-cases are investigated to cover various parameter arrangements and nonlinear properties. The resultant solutions are then generalized giving a complete family of traveling wave solutions that captures the intricate dynamics of the equation. Graphical representations are also presented to visualize the impact of different parameters on the solution behavior. The research not only generalizes the scope of classical traveling wave analysis but also illustrates the flexibility and capability of the HBM–Extended Riccati approach in solving sophisticated nonlinear differential equations.

Keywords

Sharma–Tasso–Olver equation

Travelling wave solutions

Homogeneous balance method

Extended Riccati equation

Nonlinear differential equations

Funding

The authors did not receive any funding for this research.

Conflict of interest

Both the authors declare that they have no conflicts of interest.

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