Averaging principle for the Schrödinger equations

DOI10.3934/dcdsb.2017089zbMath1364.35030OpenAlexW2596140531MaRDI QIDQ521488

Yong Li, Peng Gao

Publication date: 11 April 2017

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2017089

zbMATH Keywords

rapidly oscillating potentialcubic nonlinear Schrödinger equationsrapidly oscillating forcestable manifold and unstable manifold

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Almost and pseudo-almost periodic solutions to PDEs (35B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Averaging method for ordinary differential equations (34C29) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items

Recurrent solutions of the derivative Ginzburg–Landau equation with boundary forces ⋮ Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component ⋮ Bogoliubov averaging principle of stochastic reaction-diffusion equation ⋮ Averaging principle for stochastic Kuramoto-Sivashinsky equation with a fast oscillation ⋮ Recurrent solutions of the Schrödinger-KdV system with boundary forces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost periodic solutions and global attractors of nonautonomous Navier-Stokes equations.
• Averaging principle for quasi-geostrophic motion under rapidly oscillating forcing
• Low-dimensional chaos in a driven damped nonlinear Schrödinger equation
• Finite dimensional behavior for weakly damped driven Schrödinger equations
• Geometric theory of semilinear parabolic equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• Dynamics of quasi-geostrophic fluid motion with rapidly oscillating Coriolis force
• Generalization of the second Bogolyubov's theorem for non-almost periodic systems
• Averaging method in non-linear mechanics
• Non-linear semi-groups
• Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain
• Nonlinear Schrödinger evolution equations
• Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides
• A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain
• An Introduction to Partial Differential Equations
• A JUSTIFICATION OF THE AVERAGING METHOD FOR ABSTRACT PARABOLIC EQUATIONS
• Correlations between Chaos in a Perturbed Sine-Gordon Equation and a Truncated Model System

This page was built for publication: Averaging principle for the Schrödinger equations