Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations

DOI10.2977/prims/1195143611zbMath0945.35083OpenAlexW2083182912MaRDI QIDQ1974557

Pavel I. Naumkin, Nakao Hayashi, Hidetake Uchida

Publication date: 15 October 2000

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195143611

zbMATH Keywords

Cauchy problemgauge transformationnonlinear Schrödinger equationsphase functiontime decay estimateexistence of modified scattering states

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (10)

Well-posedness for a quadratic derivative nonlinear Schrödinger system at the critical regularity ⋮ Blow-up solutions for mixed nonlinear Schrödinger equations ⋮ The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension ⋮ Remarks on global behavior of solutions to nonlinear Schrödinger equations ⋮ Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data ⋮ Lower bounds of the lifespan of small data solutions to the nonlinear Schrödinger equations ⋮ Asymptotic behavior of solutions to Schrödinger equations with a subcritical dissipative nonlinearity ⋮ Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation ⋮ Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations ⋮ Asymptotics of odd solutions for cubic nonlinear Schrödinger equations

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• Global existence of solutions for nonlinear schrödinger equations in one space dimension
• On the nonlinear Schrodinger equations of derivative type
• Scattering theory and large time asymptotics of solutions to the Hartree type equations with a long range potential

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