A numerical and symbolical approximation of the Nonlinear Anderson Model
arXiv:0912.3906 · doi:10.1088/1367-2630/12/6/063035
Abstract
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we obtain error estimates. This approach can be useful for the solution of other nonlinear differential equations of physical relevance.
21 pages and 7 figures
References in corpus (10)
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- Destruction of Anderson localization by a weak nonlinearity
- Universal spreading of wavepackets in disordered nonlinear systems
- Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
- Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
- Rigorous Derivation of the Gross-Pitaevskii Equation
- Possible experimental manifestations of the many-body localization
- Superfluidity versus Anderson localization in a dilute Bose gas
- Best mean-field for condensates
- Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential
Cited by in corpus (13)
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
- The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
- Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices
- Effective noise theory for the Nonlinear Schrödinger Equation with disorder
- A topological approximation of the nonlinear Anderson model
- A self-consistent model of the plasma staircase and nonlinear Schrödinger equation with subquadratic power nonlinearity
- Destruction of Anderson localization in quantum nonlinear Schrödinger lattices
- Subdiffusive Lévy flights in quantum nonlinear Schrödinger lattices with algebraic power nonlinearity
- Eigenvalue repulsion estimates and some applications for the one-dimensional Anderson model
- Multifractals Competing with Solitons on Fibonacci Optical Lattice
- Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schrödinger Equation in a random potential
- Multiscale time averaging, Reloaded