The Solutions of Initial (-Boundary) Value Problems for Sharma-Tasso-Olver Equation

Abstract

A nonlinear transformation from the solution of linear KdV equation to the solution of Sharma-Tasso-Olver (STO) equation is derived out by using simplified homogeneous balance (SHB) method. According to the nonlinear transformation derived here, the exact explicit solution of initial (-boundary) value problem for STO equation can be constructed in terms of the solution of initial (-boundary) value problem for the linear KdV equation. The exact solution of the latter problem is obtained by using Fourier transformation.

Keywords

• STO equation
• nonlinear transformation
• SHB method
• solution of initial (-boundary) value problem
• linear KdV equation
• Fourier transformation