300 citations · 740 across the 24 of their papers we have counts for
12 papers · 1 filter
Numerical Direct Scattering Transform for Dark Solitons
Ilya Mullyadzhanov, Sergey Dremov, Andrey Gelash
We introduce a numerical direct scattering transform scheme for dark solitons of the nonlinear Schrodinger equation, enabling the identification and complete characterization of no…
Eigenvalue-Based Approach to Manipulate and Reconstruct Nonlinear Pulses: Towards Soliton Tomography
Sergey Dremov, Rustam Mullyadzhanov, Andrey Gelash
Soliton content of nonlinear pulses of different physical nature is universally characterized by a discrete set of eigenvalues. In an ideal channel governed by the nonlinear Schrod…
Periodic orbits underlying spatiotemporal chaos in the Lugiato-Lefever model
Andrey Gelash, Savyaraj Deshmukh, Andrey Shusharin +2
We obtain and investigate theoretically a broad family of stable and unstable time-periodic orbits-oscillating Turing rolls (OTR)-in the Lugiato-Lefever model of optical cavities.…
Manipulation of strongly interacting solitons in optical fiber experiments
Alexandre Mucci, Pierre Suret, François Copie +3
The model underlying physics of guiding light in single-mode fibers -- the one-dimensional nonlinear Schrödinger equation (NLSE), reveals a remarkable balance of the fiber dispersi…
Bi-solitons on the surface of a deep fluid: an inverse scattering transform perspective based on perturbation theory
Andrey Gelash, Sergey Dremov, Rustam Mullyadzhanov +1
We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures - bi-solitons - in the exact and approximate models for waves on the free s…
Multisoliton interactions approximating the dynamics of breather solutions
D. S. Agafontsev, A. A. Gelash, S. Randoux +1
Breather solutions are considered to be generally accepted models of rogue waves. However, breathers are not localized, while wavefields in nature can generally be considered as lo…
Numerical direct scattering transform for breathers
I. Mullyadzhanov, A. Gudko, R. Mullyadzhanov +1
We consider the model of the focusing one-dimensional nonlinear Schrödinger equation (fNLSE) in the presence of an unstable constant background, which exhibits coherent solitary wa…
Ghost interaction of breathers
Gang Xu, Andrey Gelash, Amin Chabchoub +2
Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this res…
Rogue waves with rational profiles in unstable condensate and its solitonic model
D. S. Agafontsev, A. A. Gelash
In this brief report we study numerically the spontaneous emergence of rogue waves in (i) modulationally unstable plane wave at its long-time statistically stationary state and (ii…
Solitons in a box-shaped wavefield with noise: perturbation theory and statistics
Rustam Mullyadzhanov, Andrey Gelash
We investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform…
Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves
Pierre Suret, Alexey Tikan, Félicien Bonnefoy +9
Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. Despite significant theoretical developments and o…
Strongly interacting soliton gas and formation of rogue waves
A. A. Gelash, D. S. Agafontsev
We study numerically the properties of (statistically) homogeneous soliton gas depending on soliton density (proportional to number of solitons per unit length) and soliton velocit…