The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation
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Publication:1744126
DOI10.1007/s00332-017-9426-xzbMath1390.35325OpenAlexW2769861550MaRDI QIDQ1744126
Publication date: 16 April 2018
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00332-017-9426-x
Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Riemann-Hilbert problems in context of PDEs (35Q15)
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Cites Work
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- Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method
- Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent
- Adjoint symmetry constraints of multicomponent AKNS equations.
- Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
- A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
- Long-time asymptotics for the Degasperis-Procesi equation on the half-line
- Algebro-geometric solutions to the Manakov hierarchy
- Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line
- Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data
- A Unified Approach to Boundary Value Problems
- Long-time Asymptotics for the Camassa–Holm Equation
- Scattering and inverse scattering for first order systems
- Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Nonvanishing Continuous Background
- L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
- Long-time asymptotics for the pure radiation solution of the sine—gordon equation
- Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector
- Higher order asymptotics of the modified non-linear schrödinger equation
- Trigonal curves and algebro-geometric solutions to soliton hierarchies II
- The nonlinear Schrödinger equation on the half-line
- A Riemann–Hilbert approach for the Degasperis–Procesi equation
- Adjoint Symmetry Constraints Leading to Binary Nonlinearization
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