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Soliton dynamics and scattering. (English) Zbl 1111.35054

Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume III: Invited lectures. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 459-471 (2006).
It is well-known that nonlinear dispersive equations play a prominent role in many fields of physics, includingnonlinear optics, large molecule dynamics and more. The mathematical aspects of such equations are remarkably rich, and contribute new challenging directions for mathematical physics, spectral and scattering theory. In partaicular, the problem of large dynamics of interacting solitons and more general coherent structures have achieved much interest in the last decade. In this survey, the author focuses on the problem of large time behaviour of the nonlinear Schrödinger equation, with both solitary and radiative waves appearing in the solution.
For the entire collection see [Zbl 1095.00006].

MSC:

35Q51 Soliton equations
37L50 Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems
35B40 Asymptotic behavior of solutions to PDEs
35P25 Scattering theory for PDEs
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