| Contents |
| Using Ermakov and Riccati type systems, we present how we can construct explicit solutions for the propagator for a generalized harmonic oscillator. This has applications describing the process of degenerate parametric amplification in quantum optics as well as light propagation in a nonlinear anisotropic waveguide. We also present explicit solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation, showing the existence of oscillating laser beams in a parabolic waveguide and spiral light beams in varying media. Finally, using a similar approach we show how we can construct soliton solutions for the nonautonomous nonlinear Schroedinger equation. |
|