Dr. Dionyssis Mantzavinos | Long-time asymptotics for the integrable focusing nonlinear Schrödinger

Speaker: Dr Dionyssis Mantzavinos (University of Kansas)
Date: 1st Aug 2024
Title: Long-time asymptotics for the integrable focusing nonlinear Schrödinger equation and proximity of its solutions with those of its non-integrable generalizations
Event: (PDWW01) Frontiers of Dispersive Hydrodynamics
Abstract: Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory for standard variables (Zakharov, 1968), which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. Instability growth rate increases with increase of wavenumber so that small scales blow up in arbitrary small time. To fix that problem we introduce the canonical Hamiltonian transform from original physical variables to new variables for which instability is absent and dynamical equations are well-posed.

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