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Lev Ostrovsky, Colloquium
September 22, 2016 @ 4:00 pm - 5:00 pm
Tea at 3:30 pm
Title: Perturbation theory of solitons and their behavior as particles
Abstract: The term “soliton” is now widely known even among the non-specialists. Solitary waves on water surface were first observed by J. Scott Russell in 1834. In 1967 M. Kruskal and N. Zabusky have numerically shown that solitary waves can nonlinearly interact in such a way that after the interaction they remain unchanged, with only an additional time delay. Such a behavior is characteristic of elastic collision of material particles, thus the term “soliton” was introduced. Another breakthrough was the discovery of new exact methods of solving a certain class of equations, especially the so-called inverse scattering method. However, exact description of soliton dynamics is possible almost exclusively for fully integrable equations, and even for them it is often difficult to interpret the formal result for more than two solitons. Thus, different perturbation schemes for solitons were developed since 1970s.