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

DOI10.1016/j.jde.2019.11.062zbMath1435.35270arXiv1903.04857OpenAlexW2994545534MaRDI QIDQ2306679

Lin Huang, Jonatan Lenells

Publication date: 24 March 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.04857

zbMATH Keywords

asymptoticsRiemann-Hilbert probleminitial value problemSasa-Satsuma equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (14)

Higher Order Airy and Painlevé Asymptotics for the mKdV Hierarchy ⋮ Long time and Painlevé-type asymptotics for the Sasa-Satsuma equation in solitonic space time regions ⋮ The initial-boundary value problems of the new two-component generalized Sasa-Satsuma equation with a \(4\times 4\) matrix Lax pair ⋮ Painlevé-type asymptotics of an extended modified KdV equation in transition regions ⋮ Dispersive wave propagation of the nonlinear Sasa-Satsuma dynamical system with computational and analytical soliton solutions ⋮ Nonlinear physical complex Hirota dynamical system: construction of chirp free optical dromions and numerical wave solutions ⋮ Long-time asymptotic behavior for the matrix modified Korteweg-de Vries equation ⋮ Painlevé asymptotics for the coupled Sasa-Satsuma equation ⋮ A two-component Sasa-Satsuma equation: large-time asymptotics on the line ⋮ Large and infinite-order solitons of the coupled nonlinear Schrödinger equation ⋮ Asymptotics behavior for the integrable nonlinear Schrödinger equation with quartic terms: Cauchy problem ⋮ Asymptotics of solutions to a fifth-order modified Korteweg–de Vries equation in the quarter plane ⋮ Long-time asymptotics for an integrable evolution equation with a \(3 \times 3\) Lax pair ⋮ Application of the nonlinear steepest descent method to the general coupled nonlinear Schrödinger system

Cites Work

• Unnamed Item
• Interaction properties of complex modified Korteweg-de Vries (mKdV) solitons
• Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane
• Matrix Riemann-Hilbert problems with jumps across Carleson contours
• The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The unified transform method for the Sasa–Satsuma equation on the half-line
• Inverse scattering on the line
• New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
• Long-time asymptotics for the Sasa–Satsuma equation via nonlinear steepest descent method
• Construction of solutions and asymptotics for the sine-Gordon equation in the quarter plane
• The Riemann–Hilbert Problem and Inverse Scattering
• Airy and Painlevé asymptotics for the mKdV equation

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