The nonlinear steepest descent approach for long time behavior of the two-component coupled Sasa-Satsuma equation with a $5\times 5$ Lax pair

Abstract

Under investigation in this work is the coupled Sasa-Satsuma equation, which can describe the propagations of two optical pulse envelopes in birefringent fibers. The Riemann-Hilbert problem for the equation is formulated on the basis of the corresponding $5\times 5$ matrix spectral problem, which allows us to present a suitable representation for the solution of the equation. Then the Deift-Zhou steepest descent method is used to analyze the long time behavior of the coupled Sasa-Satsuma equation.

arXiv comment22 pages, 5 figures

References in corpus (13)

• The Nonlinear Schrödinger Equation on the Interval
• Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
• A new nonlocal nonlinear Schroedinger equation and its soliton solutions
• The Unified Method: I Non-Linearizable Problems on the Half-Line
• Initial-boundary value problems for integrable evolution equations with $3\times 3$ Lax pairs
• Long-time asymptotic for the derivative nonlinear Schrödinger equation with decaying initial value
• Binary Darboux Transformation for the Sasa-Satsuma Equation
• Squared Eigenfunctions for the Sasa-Satsuma Equation
• Multisoliton solutions and integrability aspects of coupled nonlinear Schrodinger equations
• Long-time asymptotics for the Hirota equation on the half-line
• $L$-functions for families of generalized Kloosterman sums and $p$-adic differential equations
• An efficient explicit full-discrete scheme for strong approximation of stochastic Allen-Cahn equation
• Long-time behavior for the Cauchy problem of the 3-component Manakov system