The N-soliton solutions to the Hirota and Maxwell-Bloch equation via the Riemann-Hilbert approach

In this paper, we study the N-soliton solutions for the Hirota and Maxwell-Bloch equation with physical meaning. From the Lax pair and Volterra integral equations, the Riemann-Hilbert problem of this integrable equation is constructed. By solving the matrix Riemann-Hilbert problem with the condition of no reflecting, the N-soliton solutions for the Hirota and Maxwell-Bloch equation are obtained explicitly. Finally, we simulate the three-dimensional diagram of |E| with 2-soliton solutions and the motion trajectory of t-axis in the case of different z.