Department of Mathematics and Statistics, San Diego State University

Seminars on Differential and Difference Equations,

and Dynamical Systems

Dynamical reduction for trapped solitons I

Ricardo Carretero, Mathematics and Statistics, SDSU

I present a couple of methods to reduce the dynamics of trapped solitary waves in the nonlinear Schroedinger equation (NLS). The reduction consists on describing the behavior of the trapped solitons (originally a PDE) by a set of ODEs on the soliton's parameters. The first method exploits conserved quantities (mass and energy) and the second uses a variational formulation for the NLS. The resulting ODEs can then be treated using standard dynamical systems machinery to study the dynamical behavior of the original soliton. I will also, if time allows, show how these ideas can be used to treat chains of coupled solitons within the framework of fiber optics and condensed matter physics.

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