Showing papers by "E. A. Kuznetsov published in 1996"
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 Article•
107 citations
TL;DR: In this article, the authors apply a variational procedure to Gaussian beams, leading to a reduced system of ordinary differential equations that describe the characteristic spatiotemporal evolutions of the chirped pulse.
Abstract: The self-focusing of ultrashort optical pulses in a nonlinear medium with normal dispersion is examined. We demonstrate that chirping the pulse initially can strongly increase the achievable peak intensity by competing with the splitting of the pulse in the time domain. On the one hand, we apply a variational procedure to Gaussian beams, leading to a reduced system of ordinary differential equations that describe the characteristic spatiotemporal evolutions of the chirped pulse. On the other hand, when the chirp induces a temporal compression of the pulse, it is shown by means of exact analytical estimates that a transverse collapse can never occur. In the opposite situation, i.e., when the chirp forces the pulse to expand temporally while it shrinks in the transverse diffraction plane, we display numerical evidence that chirping can generate highly spiky electric fields. We further describe the splitting process that takes place near the self-focusing finite distance of propagation and discuss the question of the ultimate occurrence of a collapse-type singularity.
45 citations
TL;DR: This lecture is a review of recent results (obtained mainly by the author and his co-authors) in the wave collapse theory with applications to plasma physics, fluid dynamics and nonlinear optics as well.
Abstract: This lecture is a review of recent results (obtained mainly by the author and his co-authors) in the wave collapse theory with applications to plasma physics, fluid dynamics and nonlinear optics as well. The main attention in the review is paid to the qualitative reasons of the wave collapse and to the exact methods based on the integral estimations. Both approaches are applied to both the nonlinear Schrodinger equation and the two-dimensional generalized Benjamin-Ono equation which describes self-focusing of low-frequency oscillations in the boundary layer. (c) 1996 American Institute of Physics.
34 citations
TL;DR: Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schr{umlt o}dinger equation with mixed-sign dispersion are investigated and it is shown that localized solutions to this equation cannot collapse in finite time.
Abstract: Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schr{umlt o}dinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called {ital critical} dimension cannot collapse in finite time in the sense that their transverse (anomalously dispersing) and longitudinal (normally dispersing) extensions never vanish. Solutions defined at the {ital supercritical} dimension are proved to exhibit a nonvanishing mean longitudinal size, and cannot transversally collapse if they are assumed to shrink along each spatial direction. {copyright} {ital 1996 The American Physical Society.}
20 citations
TL;DR: In this article, it is shown that in a model with a constant growth rate cracks can form webs with triple vertices and the fourth order vertices are rare and can appear as a result of scattering of triple vertice with each other.
16 citations
TL;DR: In this article, the self-focusing of ultra short optical pulses in a nonlinear medium with normal (i.e., negative) group-velocity dispersion is investigated, and it is explicitly shown that the pulse spreads out along the "time-direction" and ultimately splits up.
Abstract: The self-focusing of ultra short optical pulses in a nonlinear medium with normal (i.e., negative) group-velocity dispersion is investigated. By using a combination of various techniques like virial-type arguments and self-similar transformations, we obtain strong evidence suggesting that a pulse propagating in a nonlinear medium with normal dispersion will not collapse to a singularity in the transverse diffraction plane. It is explicitly shown that the pulse spreads out along the "time-direction" and ultimately splits up. The analytical results are supported by direct numerical solutions.
2 citations