Riemann-Hilbert approach and N-soliton solutions for a new four-component nonlinear Schrödinger equation

2020/01/12 by Zhou, Xin-Mei, Tian, Shou-Fu, Yang, Jin-Jie +1
#Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2001.03865

Abstract

A new four-component nonlinear Schrödinger equation is first proposed in this work and studied by Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a 5×5 matrix spectral problem for the four-component nonlinear Schrödinger equation. Then based on the Lax pair, we analyze the spectral problem and the analytical properties of the Jost functions, from which the Riemann-Hilbert problem of the equation is successfully established. Moreover, we obtain the N-soliton solutions of the equation by solving the Riemann-Hilbert problem without reflection. Finally, we derive two special cases of the solutions to the equation for N=1 and N=2, and the local structure and dynamic behavior of the one-and two-soliton solutions are analyzed graphically.

Related

• Riemann-Hilbert approach and N-soliton solutions for the three-component coupled Hirota equations
• Riemann-Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrodinger equation in an optical fiber
• Construction of multiple soliton solutions of the quintic nonlinear Schrodinger equation
• Riemann-Hilbert approach for multi-soliton solutions of a fifth-order nonlinear Schrodinger equation
• Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger system and its soliton solutions