300 citations · 740 across the 24 of their papers we have counts for
25 papers
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…
Hybridization of Kerr Solitons in Coupled Microresonators
Alena Kolesnikova, Ivan Pshenichnyuk, Andrey Gelash
Recent advances in manufacturing photonic integrated devices enable efficient coupling between high-Q microresonators in both linear and nonlinear regimes, creating a tunable, comp…
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.…
Copper-impurity-free photonic integrated circuits enable deterministic soliton microcombs
Xinru Ji, Xurong Li, Zheru Qiu +5
Chip-scale optical frequency combs based on microresonators (microcombs) enable GHz-THz repetition rates, broad bandwidth, compactness, and compatibility with wafer-scale manufactu…
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…
Soliton Gas: Theory, Numerics and Experiments
Pierre Suret, Stephane Randoux, Andrey Gelash +3
The concept of soliton gas was introduced in 1971 by V. Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In t…
Right and left inverse scattering problems formulations for the Zakharov-Shabat system
Alexander Chernyavsky, Leonid Frumin, Andrey Gelash
We consider right and left formulations of the inverse scattering problem for the Zakharov-Shabat system and the corresponding integral Gelfand-Levitan-Marchenko equations. Both fo…
Vector breathers in the Manakov system
Andrey Gelash, Anton Raskovalov
We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dim…
Bound-state soliton gas as a limit of adiabatically growing integrable turbulence
D. S. Agafontsev, A. A. Gelash, R. I. Mullyadzhanov +1
We study numerically the integrable turbulence in the framework of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach called the…
Lump chains in the KP-I equation
Charles Lester, Andrey Gelash, Dmitry Zakharov +1
We construct a broad class of solutions of the KP-I equation by using a reduced version of the Grammian form of the -function. The basic solution is a linear periodic chain of l…
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…
Direct scattering transform: catch soliton if you can
Andrey Gelash, Rustam Mullyadzhanov
Direct scattering transform of nonlinear wave fields with solitons may lead to anomalous numerical errors of soliton phase and position parameters. With the focusing one-dimensiona…
Bound state soliton gas dynamics underlying the noise-induced modulational instability
Andrey Gelash, Dmitry Agafontsev, Vladimir Zakharov +3
We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the…
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…
Formation of rogue waves from the locally perturbed condensate
A. A. Gelash
The one-dimensional focusing nonlinear Schrodinger equation (NLSE) on an unstable condensate background is the fundamental physical model, that can be applied to study the developm…
Complete Hamiltonian formalism for inertial waves in rotating fluids
A. A. Gelash, V. S. L'vov, V. E. Zakharov
Complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluid. Resonance three-wave interaction processes -- decay instability and confluence of t…
On the nonlinear stage of Modulation Instability
V. E. Zakharov, A. A. Gelash
We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing Nonlinear Schrödinger Equation. We find a general N-solitonic solution o…