On solutions on the initial value problem for the nonlinear Schrödinger equations

DOI10.1016/0022-1236(87)90002-4zbMath0657.35033OpenAlexW1987419180MaRDI QIDQ1110709

Nakao Hayashi, Kuniaki Nakamitsu, Masayoshi Tsutsumi

Publication date: 1987

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(87)90002-4

zbMATH Keywords

smoothinitial value problemnonlinear opticsplasma physicsnonlinear Schrödingerregularizing effectnonrelativistic quantum physics

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial value problems for nonlinear higher-order PDEs (35G25) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global existence of small solutions to nonlinear evolution equations
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Classical solutions of nonlinear Schrödinger equations
• Classical solutions of nonlinear Schrödinger equations in higher dimensions
• On the initial value problem for a nonlinear Schrödinger equation
• Weighted Sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations
• Nonlinear scattering theory at low energy: Sequel
• Abstract non linear wave equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Decay and scattering of solutions of a nonlinear Schrödinger equation
• Time dependent nonlinear Schrödinger equations
• On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension
• Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
• The asymptotic behavior of nonlinear Schrödinger equations
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Equations de Schrödinger non linéaires en dimension deux

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