Long-time asymptotics and the bright \(N\)-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach
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Publication:1698366
DOI10.1016/j.nonrwa.2017.10.014zbMath1387.35056OpenAlexW2769640776MaRDI QIDQ1698366
Publication date: 15 February 2018
Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.nonrwa.2017.10.014
Asymptotic behavior of solutions to PDEs (35B40) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)
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Cites Work
- Unnamed Item
- Unnamed Item
- Long-time asymptotic for the derivative nonlinear Schrödinger equation with step-like initial value
- On \(N\)th-order rogue wave solution to the generalized nonlinear Schrödinger equation
- Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation
- Exact solutions to the partially integrable Eckhaus equation
- Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach
- A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Nonlinear evolution equations, rescalings, model PDEs and their integrability: II
- Darboux Transformation and Soliton Solutions for Generalized Nonlinear Schrödinger Equations
- Method for Solving the Korteweg-deVries Equation
- On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation
- Integrable properties of the general coupled nonlinear Schrödinger equations
- Long‐time asymptotics of the nonlinear Schrödinger equation shock problem
- Semiclassical Limit of Focusing NLS for a Family of Square Barrier Initial Data
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