Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management
arXiv:0808.3865 · doi:10.1016/j.physleta.2008.07.013
Abstract
In this paper we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross-Pitaevskii equation is completely integrable. Under the present model, this integrability condition is completely consistent with that proposed by Serkin, Hasegawa, and Belyaeva [V. N. Serkin et al., Phys. Rev. Lett. 98, 074102 (2007)]. Furthermore, this integrability can also be explicitly shown by a transformation, which can convert the Gross-Pitaevskii equation into the well-known standard nonlinear Schrödinger equation. By this transformation, each exact solution of the standard nonlinear Schrödinger equation can be converted into that of the Gross-Pitaevskii equation, which builds a systematical connection between the canonical solitons and the so-called nonautonomous ones. The finding of this transformation has a significant contribution to understanding the essential properties of the nonautonomous solitions and the dynamics of the Bose-Einstein condensates by using the Feshbach resonance technique.
arXiv comment13 pages
References in corpus (11)
- Theory of Bose-Einstein condensation in trapped gases
- Theory of Nonlinear Matter Waves in Optical Lattices
- Dynamics of a Bright Soliton in Bose-Einstein condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential
- Strongly enhanced inelastic collisions in a Bose-Einstein condensate near Feshbach resonances
- Localized nonlinear waves in systems with time- and space-modulated nonlinearities
- Adiabatic dynamics of periodic waves in Bose-Einstein condensate with time dependent atomic scattering length
- Averaging For Solitons With Nonlinearity Management
- Similarity transformations for Nonlinear Schrodinger Equations with time varying coefficients: Exact results
- Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length
- Resonant nonlinearity management for nonlinear-Schrödinger solitons
- Feshbach Resonance and Growth of a Bose-Einstein Condensate
Cited by in corpus (9)
- Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities
- Bright and dark solitons in a quasi 1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters
- Integrable inhomogeneous NLS equations are equivalent to the standard NLS
- Transformation from the nonautonomous to standard NLS equations
- Solitons of two-component Bose-Einstein condensates modulated in space and time
- Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions
- Quantum theory of bright matter wave solitons in harmonic confinement
- Regular and chaotic Bose-Einstein condensate in an accelerated Wannier-Stark lattice
- Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation