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Asymptotic Stability of Multi-Solitons for Coupled Nonlinear Schrödinger Equations via the $\bar{\partial}$-Method
The Riemann-Hilbert problem for the focusing coupled nonlinear Schrödinger (CNLS) equation is formulated on the basis of the corresponding $3\times3$ matrix spectral problem. We remove the discrete spectrum of initial RHP with the aid of Darboux transformations. Based on the $\bar{\partial}$-steepes
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