300 citations · 740 across the 24 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
Soliton on Unstable Condensate
Vladimir Zakharov, Andrey Gelash
We construct new exact solutions of the focusing Nonlinear Schrödinger equation (NLSE). This is a soliton propagating on an unstable condensate. The Kuznetsov and Akhmediev soliton…