High-order soliton matrices for Sasa–Satsuma equation via local Riemann–Hilbert problem

By Bo Yang, Yong Chen. Nonlinear Analysis: Real world applications, 2019

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Abstract A study of high-order soliton matrices for Sasa–Satsuma equation in the framework of the Riemann–Hilbert problem approach is presented. Through a standard dressing procedure, soliton matrices for simple zeros and elementary high-order zeros in the Riemann–Hilbert problem for Sasa–Satsuma equation are constructed, respectively. It is noted that pairs of zeros are simultaneously tackled in the situation of the high-order zeros, which is different from other NLS-type equation. Furthermore, the generalized Darboux transformation for Sasa–Satsuma equation is also presented. Moreover, collision dynamics along with the asymptotic behavior for the two-solitons are analyzed, and long time asymptotic estimations for the high-order one-soliton are concretely calculated. In this case, two double-humped solitons with nearly equal velocities and amplitudes can be observed.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/59e2298f57c8fabe4585ae9f90796de525a90542