scispace - formally typeset
Search or ask a question
Author

E. A. Kuznetsov

Bio: E. A. Kuznetsov is an academic researcher from Skolkovo Institute of Science and Technology. The author has contributed to research in topics: Vorticity & Vortex. The author has an hindex of 31, co-authored 152 publications receiving 3952 citations. Previous affiliations of E. A. Kuznetsov include Novosibirsk State University & Landau Institute for Theoretical Physics.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, the stability of solitons is reviewed for nonlinear conservative media and the main attention is paid to the description of the methods: perturbation theory, inverse scattering transform, Lyapunov method.

399 citations

Journal ArticleDOI
TL;DR: In this paper, a general method for treating weakly nonlinear waves is presented based on classical perturbation theory and the Hamiltonian reduction technique, and the application of canonical variables to collisionless plasma kinetics is described.
Abstract: The Hamiltonian description of hydrodynamic type systems in application to plasmas, hydrodynamics, and magnetohydrodynamics is reviewed with emphasis on the problem of introducing canonical variables. The relation to other Hamiltonian approaches, in particular natural-variable Poisson brackets, is pointed out. It is shown that the degeneracy of noncanonical Poisson brackets relates to a special type of symmetry, the relabeling transformations of fluid-particle Lagrangian markers, from which all known vorticity conservation theorems, such as Ertel's, Cauchy's, Kelvin's, as well as vorticity frozenness and the topological Hopf invariant, are derived. The application of canonical variables to collisionless plasma kinetics is described. The Hamiltonian structure of Benney's equations and of the Rossby wave equation is discussed. Davey–Stewartson's equation is given the Hamiltonian form. A general method for treating weakly nonlinear waves is presented based on classical perturbation theory and the Hamiltonian reduction technique.

307 citations

Journal Article
TL;DR: In this paper, it is shown that when analyzing Langmuir waves, a change in the boundary conditions can lead to drastically different mathematical results, and it is also shown that change in boundary conditions may lead to different results.
Abstract: It is shown that when analyzing Langmuir waves a change in the boundary conditions can lead to drastically different mathematical results.

283 citations

Journal ArticleDOI
TL;DR: In this article, the authors combine the canonical formalism for free-surface hydrodynamics and conformal mapping to the half-plane to obtain a simple system of pseudo-differential equations for the surface shape and hydrodynamic potential.

208 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that using multi-scale expansions conventionally employed in the theory of nonlinear waves one can transform systems integrable by the IST method into other systems of this type.

200 citations


Cited by
More filters
Proceedings Article
14 Jul 1996
TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

3,530 citations

Journal ArticleDOI
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

Journal ArticleDOI
TL;DR: In this paper, a number of consequences of relativistic-strength optical fields are surveyed, including wakefield generation, a relativistically version of optical rectification, in which longitudinal field effects could be as large as the transverse ones.
Abstract: The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

1,459 citations

Journal ArticleDOI
TL;DR: A detailed overview of the physics and applications of optical dark solitons can be found in this article, where the authors discuss the instability-induced dynamics of dark-solitons in the models of generalized (i.e., non-Kerr) optical nonlinearities.

1,076 citations