Asymptotic stability of N-solitons in the cubic NLS equation

DOI10.1142/S0219891617500151zbMath1384.35050arXiv1603.02119WikidataQ115245214 ScholiaQ115245214MaRDI QIDQ4588798

Aaron Saalmann

Publication date: 2 November 2017

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

Full work available at URL: https://arxiv.org/abs/1603.02119

zbMATH Keywords

asymptotic stabilityRiemann-Hilbert problemsolitonscubic nonlinear Schrödinger equationinverse scattering\(\overline{\partial}\)-method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

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Asymptotic stability of N-solitons in the cubic NLS equation ⋮ Inverse Scattering for the Massive Thirring Model ⋮ Instability of solitary wave solutions for the nonlinear Schrödinger equation of derivative type in degenerate case ⋮ A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II

Cites Work

• Long time asymptotic behavior of the focusing nonlinear Schrödinger equation
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• Stability of multi-solitons in the cubic NLS equation
• Scattering and inverse scattering for first order systems
• L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
• Asymptotic stability of N-solitons in the cubic NLS equation
• The asymptotic stability of solitons in the cubic NLS equation on the line
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