Wave and inverse wave operators for the quadratic nonlinear Schrödinger equations in 3D

zbMath1135.35075MaRDI QIDQ2472332

Yuichiro Kawahara

Publication date: 21 February 2008

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1199719412

zbMATH Keywords

asymptoticssmall solutionswave operatorquadratic Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55)

Cites Work

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• Global existence and asymptotic behavior of small solutions to nonlinear Schrödinger equations in 3D.
• Global existence of small solutions to nonlinear evolution equations
• Nonlinear scattering theory at low energy
• Rapidly decaying solutions of the nonlinear Schrödinger equation
• Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\)
• Time decay of small solutions to quadratic nonlinear Schrödinger equations in 3D
• Remarks on scattering for nonlinear Schrödinger equations
• Lower bounds of asymptotics in time of solutions to nonlinear Schrödinger equations in 3D
• Global existence of small solutions to quadratic nonlinear schrödinger equations
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Global, small amplitude solutions to nonlinear evolution equations

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