Painlevé asymptotics for the coupled Sasa-Satsuma equation. (English) Zbl 1518.35522
Summary: 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 \(5\times 5\) matrix Riemann-Hilbert problem, it turns out that in the sector \(|x/t^{1/3}|\leq N\), \(N\) constant, the asymptotics can be expressed in terms of the solution of a coupled modified Painlevé II equation, which is related to a \(5\times 5\) matrix Riemann-Hilbert problem.
MSC:
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 34B40 | Boundary value problems on infinite intervals for ordinary differential equations |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
Keywords:
coupled Sasa-Satsuma equation; asymptotics; coupled modified Painlevé II equation; nonlinear steepest descent methodReferences:
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