Riemann-Hilbert approach and N-soliton solutions for a new
four-component nonlinear Schrödinger equation
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 $5\times5$ 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.