Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background

Abstract

In this article, the inverse scattering transform is considered for the Gerdjikov-Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann-Hilbert (RH) method. The formula of the soliton solutions are established by Laurent expansion to the RH problem. The method we used is different from computing solution with simple poles since the residue conditions here are hard to obtained. The formula of multiple soliton solutions with one high-order pole and $N$ multiple high-order poles are obtained respectively. The dynamical properties and characteristic for the high-order pole solutions are further analyzed.

34 pages

Cited by in corpus (2)

• High-order soliton matrix for the third-order flow equation of the Gerdjikov-Ivanov hierarchy through the Riemann-Hilbert method
• Inverse scattering transform and multiple high-order pole solutions for the nonlocal focusing and defocusing modified Korteweg-de Vries equation with the nonzero boundary conditions