The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions

Abstract

The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of $(N+\mathrm{1})\times (N+\mathrm{1})$ determinant and $N\times N$ determinant, and the dynamical behaviors of the single-soliton solution are displayed graphically.