Seminar “Nonlinear waves”

The next session of academician V.E. Zakharov seminar “Nonlinear waves” will be translated at https://bbb2.itp.ac.ru/b/ale-wkj-mvm on Wednesday, September 23rd at 15:30.

“Solitons in a box-shaped wavefield with noise: perturbation theory and statistics”
​Mullyadzhanov R.I.^{1,2}, Gelash A.A.^{3,4}
1 Institute of Thermophysics SB RAS, Novosibirsk 630090, Russia
2 Novosibirsk State University, Novosibirsk 630090, Russia
3 Institute of Automation and Electrometry SB RAS, Novosibirsk 630090, Russia
4 Skolkovo Institute of Science and Technology, Moscow 121205, Russia
Abstract: We investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear perturbation framework to evaluate first-order corrections of the full set of the scattering data within the integrable one-dimensional focusing nonlinear Schrödinger (NLSE) equation. The general scattering data portrait reveals nonlinear coherent structures solitons playing the key role in the wavefield evolution. Applying the developed theory to a classic box-shaped wavefield we solve the derived equations analytically for a single Fourier mode acting as a perturbation to the initial condition, thus, leading to the sensitivity closed-form expressions for basic soliton characteristics, i.e. the amplitude, velocity, phase and its position. With the appropriate
statistical averaging we model the soliton noise-induced effects resulting in compact relations for standard deviations of soliton parameters. Relying on a concept of a virtual soliton eigenvalue we derive the probability of a soliton emergence or the opposite due to noise and illustrate these theoretical predictions with direct numerical simulations of the NLSE evolution. The presented framework can be generalised to other integrable systems and wavefield patterns.

 

The preprint is available at https://arxiv.org/abs/2008.08874

Questions to Andrei Pushkarev, , +7 (909) 949-96-13
 
E.A.Kuznetsov, A.N. Pushkarev
Organizers
 

Date

Speaker Title

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