Introduction:
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Integrable nonlinear evolution equations arise in many applications, such as propagation of signals in optical fibers, water waves, Bose-Einstein condensation, two-dimensional gravity, interface motions, propagation of deformations along the DNA chain. The importance of this topic makes clear why it is important to get information on the behavior of the solutions of these equations. To achieve this aim, many methods and different techniques have been developed over the years, including the Inverse Scattering Transform (IST), the Darboux transformation, the Hirota and d-bar dressing method. In this session we intend to analyze the recent advancements in this field considering different points of view.
The session broadly focuses on nonlinear phenomena amenable of being described by means of tools derived within the theory of integrable systems, such as rogue waves and Peregrine-like solitons, dispersive shock waves, wave breaking in multidimensions, viscous conservation laws, stratified fluids, magnetic droplet solitons, isochronicity and chaos in many-body problems. In particular, the possibility to get explicit solutions by using the Inverse Scattering Transform and the use of the associated Hamiltonian structure for finding the symmetries of the system will be discussed. |
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