Embedded solitons in a χ²:χ³ system (Tom Vogel, UCF)

Abstract:  One condition for the existence of a localized soliton is that the propagation constant does not fall into the continuous spectrum of radiation modes. The tails of the solution must decay exponentially. For a multi-component system, the linear dispersion relation exhibit a multiple branch structure. It could be the case, however, that in a certain parameter region for which one of the components of the solution has oscillations (i.e. is in the continuous spectrum), there exists a discrete value of the propagation constant for which the oscillations have zero amplitude. Since this discrete value is embedded in the continuous spectrum, the associated solution is referred to as an embedded soliton. This talk discusses embedded solitons in a χ²:χ³ system. The method employed for searching such solutions is a variational method recently developed by Kaup and Malomed. This method yields estimated values for the components width, initial amplitude, and propagation constant, which are then used for initial data to find the solutions numerically. This is joint work with D.J. Kaup.

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This is an abstract of a talk to be presented at the 2004 SEAMS Workshop in Charleston, SC. For more information, visit the workshop's homepage at math.cofc.edu/SEAMS.