Formula omitted]-soliton solutions to the multi-component nonlocal Gerdjikov–Ivanov equation via Riemann–Hilbert problem with zero boundary conditions

Abstract

In this paper, based on zero curvature equation, the multi-component nonlocal reverse-time Gerdjikov–Ivanov (GI) equation is derived through nonlocal group reduction of the multi-component GI equation. Then the soliton solutions of this new multi-component nonlocal reverse-time GI equation are given with the aid of the corresponding Riemann–Hilbert problem. Especially, under the reflectless case, the N-soliton solutions of this nonlocal system are gained with a pure algebraic method, conversely, if the jump is not an identity, the solutions can only be determined by the Sokhotski–Plemelj formula.