4.5 Article

Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrodinger hierarchy with nonzero boundary conditions

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Summary: This study investigates the long-time behavior of solutions to the focusing nonlinear Schrodinger equation with symmetric, nonzero boundary conditions, exploring the nonlinear interactions between solitons and coherent oscillating structures. Combining inverse scattering transform and nonlinear steepest descent method, it reveals that the presence of a conjugate pair of discrete eigenvalues can lead to various outcomes such as soliton transmission, soliton trapping, or a mixed regime. The results are supported by accurate numerical simulations validating the soliton-induced position and phase shifts.

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