Large and infinite-order solitons of the coupled nonlinear Schrödinger equation

We study the large-order and infinite-order solitons of the coupled nonlinear Schrodinger equation with the Riemann-Hilbert method. By using the Riemann-Hilbert representation of the high-order Darboux dressing matrix, the large-order and infinite-order solitons can be analyzed directly without using inverse scattering transform. We firstly disclose the asymptotics for large-order solitons, which are divided into four different regions-the genus one region, the genus zero region, the exponential decay and the algebraic decay region. We verify the consistency between asymptotic solutions and exact solutions by the Darboux dressing method numerically. Moreover, we consider the property and dynamics for infinite-order solitons-a special limitation for the larger order solitons. It is shown that the genus one region and exponential decay region will disappear for the infinite-order solitons.