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10/09/01 Colloquium
DR. JIANKE YANG
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF VERMONT
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF VERMONT
Dynamics of Embedded Solitons in Hamiltonian Systems
Abstract: In this talk, I will review recent progress on the dynamics of perturbed embedded solitons in general Hamiltonian systems. Embedded solitons are solitary-wave solutions of nonlinear wave equations which reside at discrete points inside the continuous spectrum of the linear wave system. Previous heuristic analysis has established that embedded solitons are semi-stable, i.e., if the initial perturbation increases the embedded-soliton's energy, then the perturbed state asymptotically approaches the embedded soliton; but if the initial perturbation decreases the embedded-soliton's energy, the perturbed state decays into radiation. Here I will present a more rigorous mathematical analysis which proves this semi-stability property. I will also show that, when an embedded solition is perturbed, the amplitude of the continuous-wave radiation emitted from the perturbed state is not minimal in general. I will use the general fifth-order KdV equation as an example to illustrate the analysis, but the analysis works for general Hamiltonian systems as well.
