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

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,, +7(909) 949-96-13

E.A. Kuznetsov, A.N. Pushkarev


Speaker Title


D. Agafontsev Solitonic model of the condensate
26.05.2021 N.N.Rosanov Towards extremely short light pulses
19.05.2021 E.A.Kuznetsov Fine structure of vortex pancakes
28.04.2021 N.M. Zubarev Two Classes of Exact Solutions of the Problem of Unsteady Plane Motion of a Fluid with the Free Surface – Formation of Singularities
14.04.2021 V.Shrira Upper-ocean Ekman currents: a new perspective on the century old problem
07.04.2021 V.E.Zakharov Formation and non-formation of singularity on the surface of ideal fluid without gravity
31.03.2021 S.Dyachenko The Tale of Two Branch Points: Singularities in 2D flows
17.03.2021 E.A.Kuznetsov Breaking in the inviscid boundary layer (continuation)
10.03.2021 A.Mailybaev Hidden spatiotemporal symmetries in turbulence: effects of Galilean invariance
03.03.2021 A.Mailybaev Hidden spatiotemporal symmetries in statistics of turbulence
24.02.2021 E.A. Kuznetsov Breaking in inviscid boundary layer
17.02.2021 A. Pushkarev About ST6 model of wind energy input and wave energy dissipation source terms in operational forecasting of ocean waves
10.02.2021 S.V. Dremov Bound Coherent Structures Propagating on the Free Surface of Deep Water
03.02.2021 Vladimir Yankov Solitons, Vortices, Sun, and Tokamaks as Statistical Attractors
27.01.2021 Gregory Falkovich Fibonacci turbulence
20.01.2021 Sergei K. Turitsyn Intermediate asymptotics in nonlinear systems and coexistence of coherent structures and linear waves
13.01.2021 S. Nazarenko Self-similar evolution in wave turbulence and non-equilibrium
14-15.12.2020 24 speakers Joint seminar “Nonlinear Waves” with Scientific Council “Nonlinear Dynamics” RAS “Nonlinear Session – 20″
02.12.2020 A. Kamchatnov Optico-mechanical analogy and number of solitons
25.11.2020 V.Sirota Stationary scaling in small-scale turbulent dynamo problem
18.11.2020 M.Onorato Thermalization and anomalous correlators in the Fermi-Pasta-Ulam-Tsingou chain
11.11.2020 E.Kochurin Numerical Simulation of Collinear Capillary-Wave Turbulence
28.10.2020 Y.Stepanyants The asymptotic approach to the description of two-dimensional soliton patterns
21.10.2020 K.Zybin No feedback is possible in small-scale turbulent magnetic field
14.10.2020 S.Vergeles Steady axial magnetic field maintained in a columnar vortex in a rotating turbulent conducting fluid
07.10.2020 A.Slunyaev Direct numerical simulation of 3D rogue waves
30.09.2020 A.Gelash Solitonic model of the condensate
23.09.2020 R.Mullyadzhanov Solitons in a box-shaped wavefield with noise: perturbation theory and statistics
16.09.2020 P.Lushnikov Motion of singularities in fluid dynamics
09.09.2020 V.E.Zakharov Are the equations of deep water with the free surface integrable?
17.06.2020 E.Pelinovsky Bottom Pressure under Waves in Shallow Waters​
10.06.2020 N.Ussembayev On some new results in the Hamiltonian theory of weakly nonlinear surface waves
03.06.2020 V.Gordin Wind in the boundary layer of the Earth’s atmosphere. Observations and a generalized Ekman-Akkerblom model. The complex coefficient of the turbulent exchange is more adequate
27.05.2020 D.Agafontsev Adiabatically growing integrable turbulence
20.05.2020 A.Minakov Long-time asymptotics for the modified Korteweg-de Vries equation with step-like initial data
13.05.2020 S. Badulin Theory of wave turbulence for satellite altimetry: wave dynamics and climatology remote sensing of sea state
29.04.2020 V. Geogjaev Quadruplet form of Hasselmann equation
22.04.2020  A. Pushkarev Nonlinear Wind Waves Generation in Straits: Laser-Like and Self-Similar Regimes
15.04.2020 D. Kachulin Soliton turbulence in approximate and exact models for deep water waves
08.04.2020 E. Kuznetsov Compressible structures in two-dimensional hydrodynamic systems
01.04.2020 A. Dyachenko Multiple Soliton Interactions on the Surface of Deep Water
25.03.2020 I. Sibgatullin Linear and nonlinear wave attractors in stratified or rotating fluids
18.03.2020 E. Mikhailov Propagation of nonlinear waves in problems of magnetic field generation in the dynamo theory
11.03.2020 A. Gelash Synchronized breather interactions
04.03.2020 E. Prosviryakov Exact solutions of the Navier-Stokes equations for describing large-scale flows of the oceans and amplification of Stokes waves in a liquid
19.02.2020 V. Zakharov Chain solitons in KP-1 equation