Similarity transformations for Nonlinear Schrodinger Equations with time varying coefficients: Exact results
arXiv:nlin/0512061 · doi:10.1016/j.physd.2006.07.002
Abstract
In this paper we use a similarity transformation connecting some families of Nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation. This transformation allows one to apply all known results for that equation to the non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, using stationary solutions of the autonomous nonlinear Schrodinger equation we can construct exact breathing solutions to multidimensional non-autonomous nonlinear Schrodinger equations. An application is given in which we explicitly construct time dependent coefficients leading to solutions displaying weak collapse in three-dimensional scenarios. Our results can find physical applicability in mean field models of Bose-Einstein condensates and in the field of dispersion-managed optical systems.
References in corpus (10)
- Dynamics of a Bright Soliton in Bose-Einstein condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential
- Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
- Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
- On the modulational stability of Gross-Pitaevskii type equations in 1+1 dimensions
- Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers
- Nonlinearity Management in Optics: Experiment, Theory, and Simulation
- On collapse in the nonlinear Schrodinger equation with time dependent nonlinearity. Application to Bose-Einstein condensates
- Measurement of the Generalized Forward Spin Polarizabilities of the Neutron
- Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
- Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate
Cited by in corpus (20)
- Nonlinear waves in -symmetric systems
- Fast optimal frictionless atom cooling in harmonic traps
- Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
- Localized nonlinear waves in systems with time- and space-modulated nonlinearities
- Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients
- Solitons with Cubic and Quintic Nonlinearities Modulated in Space and Time
- Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities
- Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrodinger equation with modulating coefficients
- Bright and dark solitons in a quasi 1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters
- Modulation of breathers in cigar-shaped Bose-Einstein condensates
- Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management
- Analytical three-dimensional bright solitons and soliton-pairs in Bose-Einstein condensates with time-space modulation
- Matter-wave solutions in the Bose-Einstein condensates with the harmonic and Gaussian potentials
- Transformation from the nonautonomous to standard NLS equations
- Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices
- Stabilization of high-order solutions of the cubic Nonlinear Schrodinger Equation
- Modulation of breathers in the three-dimensional nonlinear Gross-Pitaevskii equation
- Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein Condensates
- From Feshbach-Resonance Managed Bose-Einstein Condensates to Anisotropic Universes: Some Applications of the Ermakov-Pinney equation with Time-Dependent Nonlinearity
- Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations