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Seminar “Nonlinear waves”


Dear Colleagues,

The next session of academician V.E. Zakharov seminar
“Nonlinear Waves” will be held on Wednesday, December 1st,
15:30 Moscow time at

“Resonant interactions of vector breathers”

Anton Raskovalov and Andrey Gelash

Abstract: We study vector solitons propagating on an unstable constant background (vector breathers) theoretically in the focusing two-component one-dimensional nonlinear Schrodinger equation (Manakov system) framework. Based on the simplified inverse scattering transform technique – the dressing method, we find the exact solutions describing resonance interactions of the vector breathers. The resonance represents a three-breathers process, i.e., a fusion of two breathers into one or decay of one breather into two, such that the characteristic wave vectors and frequencies of the breathers satisfy resonance conditions. Usually, such nontrivial interactions of solitons are possible only in the three (or more than three) component systems, such as the three-wave model. In our case, the resonance interactions are possible in the two-component model with dispersion due to the presence of the background wave field. We believe that the obtained results will contribute to the studies of vector breathers interaction, which is especially important in the light of the recent theoretical and experimental progress on optical multi-component models. The work has been accepted in the “JETP Letters” journal.

Questions to Andrei Pushkarev,, +7(909) 949-96-13

E.A. Kuznetsov, A.N. Pushkarev


Speaker Title


A. Gelash Resonant interactions of vector breathers
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10.11.2021 M.Pavlov Non-diagonalisable hydrodynamic type systems integrable by Tsarev’s Generalised Hodograph Method
27.10.2021 D.Agafontsev Growing of integrable turbulence: new results
20.10.2021 M. Pavlov Non-diagonalisable Hydrodynamic Type Systems Integrable by Tsarev’s Generalised Hodograph Method
13.10.21 S.Chefranov Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 law turbulence spectrum of breaking waves
06.10.21 A.V.Mikhailov Quantisation of free associative dynamical systems. Quantisation ideals
29.09.2021 A.Kamchatnov Propagation of instability fronts in modulationally unstable systems
22.09.2021 V.Zakharov Integrable multidimensional generalizations of the chiral field model
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
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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