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03/18/02 Colloquium
DR. DAVID SATTINGER
Department of Mathematics
Utah State University and Yale University
Department of Mathematics
Utah State University and Yale University
THE KORTEWEG-deVRIES EQUATION AND SOLITARY WAVE INTERACTIONS
Abstract: The Korteweg-deVries was originally discovered by Boussinesq in his investigations of solitary water waves observed by John Scott Russell in 1834. In addition to the solitary waves, the KdV equation possesses exact multi-soliton solutions that interact elastically, with no interchange of energy, but that exhibit a scattering shift under the interaction. In this talk we will investigate, via some numerical experiments, the question of how well these multi-solitons model the interaction of ion acoustic waves in plasmas. We shall see that the interactions are highly, although not completely, elastic, but that the plasma waves exhibit scattering anomalies from the KdV waves, which can be explained by resonance phenomena. This is joint work with Yi Li, David Nicholls, and Mariana Haragus.