2026/08/05 by Wenxia Chen, Weixuan Wang, Chaosheng Zhang +1
paper · doi:10.1088/1572-9494/ae8168
published in Communications in Theoretical Physics 78(10), 105006 (IOP Publishing)
crossref created 2026/06/24 · crossref issued 2026/08/05 · crossref published 2026/08/05 · crossref published-online 2026/08/05 · crossref deposited 2026/08/05 · crossref indexed 2026/08/05 · crossref published-print 2026/10/01
Abstract We study the long-time asymptotics of the coupled Sasa–Satsuma equation, a system with a 5 × 5 Lax pair whose rigorous analysis has remained open. Using the inverse scattering transform and the ∂ ¯ -steepest descent method, we prove soliton resolution for generic Schwartz-class initial data. Precise asymptotic formulas are obtained in five distinct spacetime regions: an oscillatory zone ( x 0 , | x / t | = O ( 1 ) ) with t − 1 / 2 corrections, a soliton zone ( x > 0 , | x / t | = O ( 1 ) ) with t − 1 decay, a Painlevé zone ( | x / t 1 / 3 | = O ( 1 ) ) described by the classical Painlevé II equation, and two transition zones connecting them (detailed in the appendix). The solution decomposes into a finite sum of breathers and solitons plus a decaying radiation, and multi-soliton/breather states are asymptotically stable under perturbations.