Growth and oscillations of solutions of nonlinear Schrödinger equation

DOI10.1007/BF02099448zbMath0862.35112OpenAlexW2034295531MaRDI QIDQ1924020

Sergej B. Kuksin

Publication date: 13 October 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099448

zbMATH Keywords

Dirichlet boundary conditionsnonlinear Schrödinger equationdynamical systemtime-space oscillationstrajectory's recurrence

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (10)

Sobolev norms explosion for the cubic NLS on irrational tori ⋮ On the theory of Weak Turbulence for the Nonlinear Schrödinger Equation ⋮ Full derivation of the wave kinetic equation ⋮ On a heavy quantum particle ⋮ Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation ⋮ Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation ⋮ A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation ⋮ Chaotic-like transfers of energy in Hamiltonian PDEs ⋮ Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs ⋮ Growth of Sobolev norms in linear Schrödinger equations as a dispersive phenomenon

Cites Work

• Unnamed Item
• Unnamed Item
• Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Nearly integrable infinite-dimensional Hamiltonian systems
• Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE's
• On squeezing and flow of energy for nonlinear wave equations
• A Remark on the Blowing-Up of Solutions to the Cauchy Problem for Nonlinear Schrodinger Equations
• Asymptotic time behaviour of nonlinear classical field equations
• The semiclassical limit of the defocusing NLS hierarchy

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