Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles

Abstract

The inverse scattering transform is considered for the complex Sharma-Tasso-Olver equation with zero boundary condition by Riemann-Hilbert method. Under the reflection-less situation, we investigate the Riemann-Hilbert problem with one high-order pole and multiple high-order poles, respectively. By Laurent expansion of the Riemann-Hilbert problem and elimination of the integral factor involved in the solution, the explicit N-soliton solutions of the equation are derived. The interactions of several various solitons are displayed and their dynamics are analyzed.