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Finite-gap approach to anomalous waves in 2 spatial dimensions and the Davey-Stewartson equation

  • Speaker:Petr Grinevich (Steklov Mathematical Institute of RAS)
  • TIME:March 23, 2023 17:00-18:00 Beijing time (16:00-17:00 Novosibirsk time)
  • LOCATION:online

Recording: https://disk.pku.edu.cn:443/link/36551E85507B5A06010718181535ABA9
Valid Until: 2027-04-30 23:59


Abstract: P. G. Grinevich, P.M. Santini.

One of the mathematical models used in the theory of anomalous (rogue) waves in the Nonlinear Schrodinger equation with special Cauchy data: at the initial time we have a small perturbation of the constant solution, corresponding to the unstable background. In the spatially-periodic setting, the finite-gap method is used. In the previous papers was demonstrated that due to the presence of a small parameter in this problem, namely the amplitude of initial perturbation, the finite-gap formulas can be essentially simplified in the leading order. These leading-order solutions are in close agreement with the results of numerical simulations.

In the present work, we show that this approach can be applied to the focusing Davey-Stewardson 2 equation, which is a 2+1 dimensional integrable analog of the Nonlinear Schrodinger equation, admitting rogue waves type solutions. Formulas expressing the leading order approximation in terms of elementary functions of Cauchy data are obtained in the doubly-periodic setting.


Bio: Petr Grinevich is a leading scientific researcher at the Steklov Mathematical Institute, RAS; he also has part-time positions at the Landau Institute of Theoretical Physics, RAS, and Lomonosov Moscow State University. Scientific interests: Solition equations, including algebro-geometric method of integration, scattering theory.