Pulses with relativistic and pseudo-relativistic aspirations

Lundie, MJ; Lancaster, G; Hodgkinson, TF; Christian, JM; Mcdonald, GS; Chamorro-Posada, P

Abstract

Temporal solitons are robust self-localizing pulses that play a pivotal role in modern understandings of nonlinear wave phenomena. Here, we propose a new approach for describing pulses in dispersive nonlinear systems. By retaining the fuller generality of the underlying Helmholtz formulation, one may go beyond conventional modelling (which anticipates slowly-varying field envelopes) to capture novel and potentially exploitable physical effects. While specific attention is paid to guided-wave optics, we believe these results are universal in nature and can be applied in a wide range of contexts, such as plasmas and water waves. Several distinct classes of exact solution family (continuous waves, solitons, cnoidal waves) are derived. The stability of these solutions is then investigated with analytical and semi-analytical methods, and one can sometimes deploy inverse-scattering theory. The fully second-order governing equation may be integrated using fast computational techniques, and extensive numerical analysis is used to test theoretical predictions.

Citation

Lundie, M., Lancaster, G., Hodgkinson, T., Christian, J., Mcdonald, G., & Chamorro-Posada, P. (2011, July). Pulses with relativistic and pseudo-relativistic aspirations. Presented at Waves 2011 - 10th International Conference on Mathematical and Numerical Aspects of Waves, Vancouver, Canada

• Presentation Conference Type: Lecture
• Conference Name: Waves 2011 - 10th International Conference on Mathematical and Numerical Aspects of Waves
• Conference Location: Vancouver, Canada
• Start Date: Jul 25, 2011
• End Date: Jul 29, 2011
• Publication Date: Jul 25, 2011
• Deposit Date: Oct 12, 2011
• Publicly Available Date: Apr 5, 2016
• Publisher URL: http://www.sfu.ca/WAVES/
• Additional Information: Event Type : Conference