Lundie, MJ, Lancaster, G, Hodgkinson, TF, Christian, JM, Mcdonald, GS and Chamorro-Posada, P 2011, Pulses with relativistic and pseudo-relativistic aspirations , in: Waves 2011 - 10th International Conference on Mathematical and Numerical Aspects of Waves, 25-29 July, 2011, Vancouver, Canada.
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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.
|Item Type:||Conference or Workshop Item (Lecture)|
Media, Digital Technology and the Creative Economy
Subjects outside of the University Themes
|Schools:||Schools > School of Computing, Science and Engineering
Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC)
|Journal or Publication Title:||Conference Proceedings|
|Publisher:||Pacific Institute for the Mathematical Sciences (PIMS)|
|Depositing User:||GS McDonald|
|Date Deposited:||12 Oct 2011 11:25|
|Last Modified:||30 Nov 2015 23:55|
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