On Integrability of Nonautonomous Nonlinear Schroedinger Equations

Abstract

We show, in general, how to transform the nonautonomous nonlinear Schroedinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is outlined. A few simple integrable systems are discussed.

15 pages, no figures

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• Degenerate Parametric Amplification of Squeezed Photons: Explicit Solutions, Statistics, Means and Variances
• On a Hidden Symmetry of Quantum Harmonic Oscillators
• The Riccati System and a Diffusion-Type Equation