Christian, J M, McDonald, G S, Hodgkinson, T F and Chamorro-Posada, P 2012, 'Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves ' , Physical Review A, 86 (2) , 023838.

Preview

PDF - Submitted Version Download (3387kB) | Preview

Abstract

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors.

Actions (login required)