Perturbation theory for the Nonlinear Schroedinger Equation with a random potential

Abstract

A perturbation theory for the Nonlinear Schroedinger Equation (NLSE) in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on small denominators was developed. It was shown that the number of terms grows exponentially with the order. The results of the perturbation theory are compared with numerical calculations. An estimate on the remainder is obtained and it is demonstrated that the series is asymptotic.

30 pages, 7 figures, accepted to Nonlinearity

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Cited by in corpus (30)

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• Asymptotic quantum many-body localization from thermal disorder
• Nonlinear waves in disordered chains: probing the limits of chaos and spreading
• Spreading for the generalized nonlinear Schroedinger equation with disorder
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Nonlinear lattice waves in heterogeneous media
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• A numerical and symbolical approximation of the Nonlinear Anderson Model
• Effective noise theory for the Nonlinear Schrödinger Equation with disorder
• Scaling perspective on Intramolecular vibrational energy flow: analogies, insights, and challenges
• On the local nature and scaling of chaos in weakly nonlinear disordered chains
• Double humped states in the nonlinear Schroedinger equation with a random potential
• Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices
• Long-time Anderson Localization for the Nonlinear Schrodinger Equation Revisited
• Classical and quantum systems: transport due to rare events
• Dynamical thermalization of Bose-Einstein condensate in Bunimovich stadium
• Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields
• Scaling of Chaos in Strongly Nonlinear Lattices
• Eigenvalue repulsion estimates and some applications for the one-dimensional Anderson model
• Multifractals Competing with Solitons on Fibonacci Optical Lattice
• Glassy dynamics in strongly anharmonic chains of oscillators
• An eigensystem approach to Anderson localization for multi-particle systems
• Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds
• Diffusion bound for the nonlinear Anderson model
• Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schrödinger Equation in a random potential
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• Multiscale time averaging, Reloaded