In this Letter we introduce a systematic perturbation method for analyzing the e ect of small perturbations on critical self focusing by reducing the perturbed critical nonlinear Schrodinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simpli ed, depending on whether PNLS is power conserving ...

The one-dimensional Schrr odinger equation is considered when the potential and its rst moment are absolutely integrable. The potential is uniquely constructed in terms of the scattering data consisting of the reeection coeecient from the right (left) and the knowledge of the potential on the right (left) half line of the real axis. Hence, neither the bound state energies nor the bound state no...

We investigate rescaling transformations for the Vlasov-Poisson and Euler-Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion eeects. The method is also used for studying the long time behaviour of the solutions and can be applied to other models in kinetic theory (2-dimensional symmetric Vlasov-Poisson system with an external magne...

We study the semiclassical limit for the following system of Maxwell-Schrr odinger equations: waves for the nonlinear Schrr odinger equation interacting with the electrostatic eld: the unknowns v and represent the wave function associated to the particle and the electric potential respectively. By using localized energy method, we construct a family of positive radially symmetric bound states (...

We obtain the most general form of the vector-potential of the electromagnetic eld A enabling separation of variables in the (1+2)-dimensional Schrr odinger equation (SE). Using this result we have carried out variable separation for a class of Schrr odinger equations that contains as particular cases SE with Coulomb scalar potential and SE for a particle interacting with the constant magnetic ...

In this paper we reconsider in the light of the Nelson stochastic mechanics the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probabil ity densities always relax in time toward the quantum mechanical density j j derived from the Schr odinger equation The analysis of a few general propositions and of some physical examples show that the ch...

The work presented in this Thesis is the result of close collaboration with several scientists, and the main part of the work has been published before in the articles 1{17], and the conference proceedings 18{26] or is going to be published 27]. The most important 13 articles 1{13] form the core of the Thesis. The Thesis consists of a review, the purpose of which is to relate the 13 articles an...

\Nonlinear Schrr odinger Equations, Wavelength Divison Multiplexing and Four Wave Mixing" In the limit of large frequency spacing the multisoliton solutions of the nonlinear Schrr odinger equation (NLS), which models the evolution of nonlinear waves in optical bers, are investigated. In Fourier space the individual pulses are found to always be widely separated, and hence can be easily, measure...

The ared horn is modeled assuming that Webster's horn equation is satis ed. Any shape can be assumed for the wavefront within the horn. This paper presents a technique for solving Webster's horn equation as follows: The equation is converted to the form of the Schrodinger wave equation used for one-dimensional particle scattering. The horn characteristics can then be obtained directly in terms...