2025/01/06 by Yang Zhenzhen, Huan Liu, Yang, Zhenzhen +3
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Numerical methods for differential equations #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2501.02719
We delve into the inverse scattering transform of the real-valued vector modified Korteweg--de Vries equation, emphasizing the challenges posed by N pairs of higher-order poles in the transmission coefficient and the enhanced spectral symmetry stemming from real-valued constraints. Utilizing the generalized vector cross product, we formulate an (n+1)×(n+1) matrix-valued Riemann--Hilbert problem to tackle the complexities inherent in multi-component systems. We subsequently demonstrate the existence and uniqueness of solutions for a singularity-free equivalent problem, adeptly handling the intricacies of multiple poles. In reflectionless cases, we reconstruct multi-pole soliton solutions through a system of linear algebraic equations.