Solutions to the nonlinear Schrödinger equation with sequences of initial data converging to a Dirac mass

DOI10.1016/j.physd.2010.07.006zbMath1211.37086OpenAlexW2036731688MaRDI QIDQ611859

J. P. Newport, Kenneth T.-R. McLaughlin

Publication date: 14 December 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2010.07.006

zbMATH Keywords

integrable systemsnonlinear partial differential equationsRiemann-Hilbert analysisscattering and inverse scattering theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

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Cites Work

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• On the Dirac delta as initial condition for nonlinear Schrödinger equations
• Long-time asymptotics for integrable systems. Higher order theory
• Scattering and inverse scattering for first order systems
• Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space