1L.V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russia 2Department of Photonics and Laser Technology, Siberian Federal University, Krasnoyarsk 660079, Russia 3Laboratory for Nonlinear Optics and Spectroscopy, Siberian Federal University, Krasnoyarsk 660079, Russia 4Faculty of Physics and International Laser Center, M. V. Lomonosov Moscow State University, Moscow 119992, Russia *Corresp...

Recent advances in table-top, ultrahigh intensity lasers have led to significant renewed interest in the classic problem of Thomson scattering. An important current application of these scattering processes is the generation of ultrashort-pulse-duration x rays. In this tutorial, the classical theory of nonlinear Thomson scattering of an electron in an intense laser field is presented. It is fou...

Abstract. The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beamlike solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homog...

This research program is aimed at deriving and elucidating non-iterative approaches to the nonlinear inverse scattering problem including multiple scattering. They are applicable to certain classes of scatterers which go beyond the class of Born-approximable scatterers (they form a broader class). Two variants of the problem are of interest: 1) The support inversion or shape reconstruction prob...

Inverse Scattering methods for solving integrable nonlinear p.d.e. found their limits as soon as one tried to solve with them new boundary value problems. However, some of these problems, e.g. the quarter-plane problem, can be solved (e.g. by Fokas linear methods), for related linear p.d.e., (e.g. LKdV). It is shown here that a nonlinear algebraic inverse scattering method, which we already app...

A number of third order nonlinear processes can occur in single-mode fibres and an 8 understanding of such phenomena is almost a prerequisite for actual lightwave-system designers. 9 In this paper we review the main limitations imposed by several nonlinear effects, namely the self10 and cross-phase modulation, four-wave mixing, stimulated Raman scattering and stimulated 11 Brillouin scattering,...

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy [10, 11] extends to the threshold energy in...

We find the general solution to Polchinski’s classical scattering equations for 1 + 1 dimensional string theory. This allows efficient computation of scattering amplitudes in the standard Liouville × c = 1 background. Moreover, the solution leads to a mapping from a large class of time-dependent collective field theory backgrounds to corresponding nonlinear sigma models. Finally, we derive recu...