Asymptotics for the Sasa-Satsuma equation in terms of a modified Painleve II transcendent

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Huang, Lin¹  Lenells, Jonatan² 

[1] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Peoples R China

[2] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

关键词: Sasa-Satsuma equation;    Riemann-Hilbert problem;    Asymptotics;    Initial value problem;   

DOI  :  10.1016/j.jde.2019.11.062

来源: Elsevier

【 摘 要 】

We consider the initial-value problem for the Sasa-Satsuma equation on the line with decaying initial data. Using a Riemann-Hilbert formulation and steepest descent arguments, we compute the long-time asymptotics of the solution in the sector vertical bar x vertical bar <= Mt(1/3) constant. It turns out that the asymptotics can be expressed in terms of the solution of a modified Painleve II equation. Whereas the standard Painleve II equation is related to a 2 x 2 matrix Riemann-Hilbert problem, this modified Painleve II equation is related to a 3 x 3 matrix Riemann-Hilbert problem. (C) 2019 The Authors. Published by Elsevier Inc.

【 授权许可】

Free