Showing papers by "Vladimir E. Zakharov published in 1975"
875 citations
TL;DR: In this paper, the S theory is proposed to limit the amplitude of the exponentially growing spin wave in ferromagnetic dielectric dielectrics by pairing of waves with equal and opposite wave vectors, which leads to the violation of phase relationships.
Abstract: The nonlinear stage of the parametric excitation of spin waves in ferromagnetic dielectrics is reviewed. The main nonlinear mechanism which limits the amplitude of the exponentially growing waves is the pairing of waves with equal and opposite wave vectors, which leads to the violation of phase relationships. This effect is described in terms of a Hamiltonian which is diagonal in the wave pairs; The corresponding approximation is called the S theory. Within the framework of this theory, the distribution of the excited waves in κ space is singular: the waves lie on individual lines or points. Consequences of the S theory and their experimental verification are discussed in detail. Collective oscillations of a spin-wave system and the origin of the observed self-modulation of their amplitude are also considered.
149 citations
01 Nov 1975
TL;DR: In this paper, the inverse scattering problem was used to integrate certain nonlinear operators without assuming the nonlinearity to be small, and solutions were given for the decay case for resonant interactions.
Abstract: Translated from Zh. Eksp. Teor. Fiz., Pis'ma Red.; 18: No. 7, The equations for the two types of resonant interactions (decay and explosive) are given. The case for monochromatic waves is considered. The method of the inverse scattering problem was used to integrate certain nonlinear operators without assuming the nonlinearity to be small. Solutions are given for monochromatic waves and the decay case for resonant interactions. (MOW)
108 citations
62 citations
Journal Article•
39 citations
01 Jul 1975
TL;DR: In this paper, the fine structure of weak Langmuir turbulence spectra produced by induced scattering by ions is studied and the spectrum is found to be stationary only at a small turbulence level (WlnT «krD IN)(Mlm)1I2, where N is the number of particles in the Debye sphere).
Abstract: The fine structure of weak Langmuir turbulence spectra produced by induced scattering by ions is studied. The spectrum is found to be stationary only at a small turbulence level (WlnT «krD IN)(Mlm)1I2, where N is the number of particles in the Debye sphere). Otherwise the spectrum is nonstationary and consists of solitons moving in k-space and absorbed in the small-wave-number region via a Langmuir-collapse mechanism. Depending on the excitation conditions, the spectrum can be regular or can consist of discrete harmonics. The analytic deductions are confirmed by numerical calculations.
18 citations
Journal Article•
TL;DR: In this article, numerical experiments on spherically symmetric wave collapse are reported and discussed based on equations describing the time-dependent self-focusing of light and the dynamics of plasma waves in a plasma.
Abstract: Numerical experiments on spherically symmetric wave collapse are reported and discussed. The experiments are based on equations describing the time-dependent self-focusing of light and the dynamics of plasma waves in a plasma.
11 citations
Journal Article•
TL;DR: In this paper, a collapse phenomenon occurs according to the dynamical equations of a hot plasma averaged over the period of the electron plasma waves, and its self-similar nature is demonstrated.
Abstract: A collapse phenomenon occurs according to the dynamical equations of a hot plasma averaged over the period of the electron plasma waves. The evolution of the collapse is analyzed, and its self-similar nature is demonstrated. The theoretical results have been checked and confirmed in numerical experiments for two cavity configurations: planar and axisymmetric.
4 citations