Abstract
In this paper, we establish the Riemann–Hilbert problem for the non-degenerate high-order solitons of the coupled nonlinear Schrödinger equation. The dynamics of these two components q1 and q2 behave quite differently. By choosing some proper parameters, one component will have a double-hump soliton but the other one will not. Especially, this kind of high-order solitons will not satisfy the scalar nonlinear Schrödinger equation under the SU(2) symmetry. Moreover, we also give the asymptotic analysis of large t for these different components and check the asymptotic solutions and the exact solutions numerically.
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