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
Date |
Speaker | Title | |
02.06.2021 |
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 |