On the Riemann-Hilbert problem for the integrable three-coupled Hirota system with a [formula omitted] matrix Lax pair

Abstract

In this work, we will investigate a complete integrable variable coefficient three-coupled Hirota system, which possesses a generalization of fourth-order matrix spectral problem AKNS type Lax pair. With the help of the unified transform method, the initial-boundary value problems (IBVPs) of the three-coupled Hirota equation on the half-line will be discussed. In other words, one can obtain the solutions of the three-coupled Hirota equation by solving a fourth-order matrix Riemann-Hilbert problem in the complex ξ-plane. Furthermore, we will show that three spectral functions φ(ξ),ϕ(ξ) and ψ(ξ) are not independent but meet a key relationship, i.e. the so-called global relation.