The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions: soliton resolution via mixed ∂-Riemann-Hilbert problem

Abstract

In this paper, we investigate the Cauchy problem of the Sasa-Satsuma (SS) equation with initial data belonging to the Schwartz space. The SS equation is one of integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3 × 3 Lax representation. With the aid of the ∂-nonlinear steepest descent method of the mixed¯∂-Riemann-Hilbert problem, we give the soliton resolution and long-time asymptotics for the Cauchy problem of the Sasa-Satsuma equation with the existence of second-order discrete spectra in the space-time solitonic regions.