Painlevé asymptotics for the coupled Sasa-Satsuma equation

Abstract

We compute the long-time asymptotics of the solution to the Cauchy problem for coupled Sasa-Satsuma equation on the line with decaying initial data. By performing a nonlinear steepest descent arguments for an associated 5 × 5 5\times 5 matrix Riemann–Hilbert problem, it turns out that in the sector | x / t 1 / 3 | ≤ N |x/t^{1/3}|\leq N , N N constant, the asymptotics can be expressed in terms of the solution of a coupled modified Painlevé II equation, which is related to a 5 × 5 5\times 5 matrix Riemann–Hilbert problem.