The Deift–Zhou steepest descent method to long-time asymptotics for the Sasa–Satsuma equation

By Huan Liu, Xianguo Geng, Bo Xue. Journal of Differential Equations, 2018

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Abstract The initial value problem for the Sasa–Satsuma equation is transformed to a 3 × 3 matrix Riemann–Hilbert problem with the help of the corresponding Lax pair. Two distinct factorizations of the jump matrix and a decomposition of the vector-valued function ρ ( k ) are given, from which the long-time asymptotics for the Sasa–Satsuma equation with decaying initial data is obtained by using the nonlinear steepest descent method.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2be8e50184ac21d6d0298e7bbabd21120c9a1c54