Integrable Systems Seminar
Thursday, April 18, 2002, 4:00pm, 114 Physics
David Kaup (University of Central Florida)
Virtual Solitons

Abstract:

Virtual solitons are solitons (nonlinear waves) that occur in systems that normally do not have ordinary solitons. These solitons have been found in Second Harmonic Generation (SHG), for example. When first found, they were seen as poles of the reflection coefficient in the lower half complex $\zeta$-plane. (Such poles ordinarily have no significance.) Later they were connected to soliton states which are singular, and which arise from poles of the reflection coefficient in the upper half complex $\zeta$-plane of a self-adjoint problem (which should normally have NO such poles). In order to better understand the nature of virtual solitons, and the scattering data associated with them, we shall present some simple analytical examples, for which we shall have closed form solutions, and use them to attempt to clarify the above seemingly contradictory statements.

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