The Sasa-Satsuma equation with 3×3 matrix spectral problem is one of the integrable extensions of the nonlinear Schrödinger equation. In this paper, we consider the Cauchy problem of the Sasa-Satsuma equation with generic decaying initial data. Based on the Rieamnn-Hilbert problem characterization for the Cauchy problem and the ∂‾-nonlinear steepest descent method, we find qualitatively different long time asymptotic forms for the Sasa-Satsuma equation in three solitonic space-time regions:(1)For the region x<0,|x/t|=O(1), the long time asymptotic is given byq(x,t)=usol(x,t|σd(I))+t−1/2h+O(t−3/4), in which the leading term is N(I) solitons, the second term the second t−1/2 order term is soliton-radiation interactions and the third term is a residual error from a ∂‾-equation.(2)For the region x>0,|x/t|=O(1), the long time asymptotic is given byu(x,t)=usol(x,t|σd(I))+O(t−1), in which the leading term is N(I) solitons, the second term is a residual error from a ∂‾-equation.(3)For the region |x/t1/3|=O(1), the Painlevé asymptotic is found byu(x,t)=1t1/3uP(xt1/3)+O(t2/(3p)−1/2),4<p<∞, in which the leading term is a solution to a modified Painlevé II equation, the second term is a residual error from a ∂‾-equation.
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