Seminar “Nonlinear waves”

Dear Colleagues,

The next session of academician V.E. Zakharov seminar
“Nonlinear Waves” will be held on Wednesday, June 2nd,
15:30 Moscow time at https://bbb2.itp.ac.ru/b/ale-wkj-mvm

A. Gelash, D. Agafontsev, P. Suret, S. Randoux

Solitonic model of the condensate

We consider a spatially extended box-shaped wave field that consists of
a plane wave (the condensate) in the middle and equals to zero at the
edges, in the framework of the focusing one-dimensional Nonlinear
Schrodinger equation. Within the inverse scattering transform (IST)
theory, the scattering data for this wave field is presented by the
continuous spectrum of the nonlinear radiation and the soliton
eigenvalues together with their norming constants; the number of
solitons N is proportional to the box width. We remove the continuous
spectrum from the scattering data and find analytically the specific
corrections to the soliton norming constants that arise due to the
removal procedure. The corrected soliton parameters correspond to
symmetric in space N-soliton solution, as we demonstrate analytically in
the paper. Generating this solution numerically for N up to 1024, we
observe that, at large N, it converges asymptotically to the condensate,
representing its solitonic model. Our methods can be generalized for
other strongly nonlinear wave fields, as we demonstrate for the
hyperbolic secant potential, building its solitonic model as well. The
talk is an update of the presentation given by Andrey Gelash in 2020.

Questions to Andrei Pushkarev, dr.push@gmail.com, +7(909) 949-96-13

E.A. Kuznetsov, A.N. Pushkarev
Organizers