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

• Published in: Nonlinear analysis: real world applications Vol. 45; pp. 918 - 941
• Main Authors: Yang, Bo, Chen, Yong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.02.2019; Elsevier BV
• Subjects: Asymptotic analysis; Asymptotic methods; Asymptotic properties; Collision dynamics; Darboux transformation; High-order soliton solution; Hilbert space; Partial differential equations; Riemann–Hilbert problem; Solitary waves; High-order soliton solution; Asymptotic analysis; Riemann–Hilbert problem; Darboux transformation
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2018.08.004

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.