Aspects of Wave Interaction in Nonlinear Media

Doctoral thesis, 2005

Selected aspects of various types of nonlinear wave interaction are investigated. These aspects are studied in terms of models described by Nonlinear Schrödinger equations, mainly analytically and numerically, but also experimentally. The emphasis is on fundamental phenomena and mathematical methods, aiming to take full advantage of the formal analogies between different physical fields. The thesis contains ten appended papers. Paper I investigates four-wave mixing of femtosecond pulses propagating close to the zero-dispersion wavelength in optical fibers. Papers II–III investigate how a non-monotonic chirp can split a pulse in an optical fiber. Paper IV determines the ground states of a Bose-Einstein condensate described by the Gross-Pitaevskii equation by means of a variational approximation with a super-Gaussian ansatz. Paper V describes a coupled-mode theory for Bose-Einstein condensates in a harmonic double-well trap. In Papers VI, VII and IX, the Wigner transform method is used for modelling nonlinear propagation of incoherent light, and the method is applied to modulational instability of a single plane wave (Paper VI) and of two interacting plane waves (Papers VII and IX). Paper VIII applies the Wigner transform method to studying the stability of a multistream quantum plasma. Paper X treats the modulational instability of partially coherent waves by obtaining the full solution of the perturbations as an initial value problem.