ОBSERVATION OF FERMI-PASTA-ULAM-TSINGOU RECURRENCE IN OPTICAL EXPERIMENT

Recently P.G. Grinevich and P.M. Santini suggested simple approximate formulas for solving periodic Cauchy problem for the focusing Nonlnear Schrodinger Equation (NLS) under assumption that one starts from a small perturbation of the unstable condensate and the number of unstable modes is not too large. With the help of these results, optical experiments in photorefractive crystal where conducted, in which the second and third return of anomalous waves was observed. A good agreement between the experimental data and the predictions made on the basis of the NLS theory was obtained. P.G. Grinevich was supported by the Russian Science Foundation grant No. 18-11-00316.

Analysis of a Fourier-Galerkin numerical scheme for a 1D Benney-Luke-Paumond equation

We study convergence of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a nonlinear Benney-Luke-Paumond equation that models long water waves with small amplitude propagating over a shallow channel with at bottom. The accuracy of the numerical solver is checked using some exact solitary wave solutions. In order to apply the Fourier-spectral scheme in a non periodic setting, we approximate the initial value problem with x ∈ R by the corresponding periodic Cauchy problem for x ∈ [0, L], with a large spatial period L.