Transformation from the nonautonomous to standard NLS equations

Abstract

In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schrödinger (NLS) equation. An integrable condition is first obtained by the Painlevè analysis, which is shown to be consistent with that obtained by the Lax pair method. Under this condition, we present a general transformation, which can directly convert all allowed exact solutions of the standard NLS equation into the corresponding exact solutions of the nonautonomous NLS equation. The method is quite powerful since the standard NLS equation has been well studied in the past decades and its exact solutions are vast in the literature. The result provides an effective way to control the soliton dynamics. Finally, the fundamental bright and dark solitons are taken as examples to demonstrate its explicit applications.

published version, 4 pages, 2 figures

References in corpus (7)

• Formation and Propagation of Matter Wave Soliton Trains
• Dark Solitons in Bose-Einstein Condensates
• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Dynamics of a Bright Soliton in Bose-Einstein condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential
• Localized nonlinear waves in systems with time- and space-modulated nonlinearities
• Similarity transformations for Nonlinear Schrodinger Equations with time varying coefficients: Exact results
• Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management

Cited by in corpus (3)

• Bright and dark solitons in a quasi 1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters
• Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation
• Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions