Numerical Simulation of Electromagnetic Solitons and their Interaction with Matter

A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on an explicit finite-difference technique. The experiments in two dimensions simulate travelling solitary electromagnetic waves, and show their interaction with conductive walls. In particular, the classical dispersion, exhibited by the passage of a photon through a small aperture, is examined.Comment: 17 pages, 9 figure

Maxwell-Drude-Bloch dissipative few-cycle optical solitons

We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material, and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and propagation of few-cycle dissipative solitons under excitation by incident femtosecond optical pulses of relatively high energies. The broadband losses that are introduced by the medium conductivity represent the main stabilization mechanism for the dissipative few-cycle solitons.Comment: 38 pages, 10 figures. submitted to Physical Review

Nonlinear aspects of quantum plasma physics

Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects, in semiconductors and micro-mechanical systems, as well as in the next generation intense laser-solid density plasma interaction experiments and in quantum x-ray free-electron lasers. In contrast to classical plasmas, one encounters extremely high plasma number density and low temperature in quantum plasmas. The latter are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, holes) follow the Fermi-Dirac statistics. In quantum plasmas, there are new forces associated with i) quantum statistical electron and positron pressures, ii) electron and positron tunneling through the Bohm potential, and iii) electron and positron angular momentum spin. Inclusion of these quantum forces provides possibility of very high-frequency dispersive electrostatic and electromagnetic waves (e.g. in the hard x-ray and gamma rays regimes) having extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave-wave and wave-electron interactions in dense quantum plasmas. Specifically, we shall focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of 3D quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase space kinetic structures and mechanisms that can generate quasi-stationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed.Comment: 42 pages, 20 figures, accepted for publication in Physics-Uspekh

Fluid simulation studies of the dynamical behaviour of one dimensional relativistic electromagnetic solitons

A numerical fluid simulation investigation of the temporal evolution of a special class of traveling wave solution of the one dimensional relativistic cold plasma model is reported.The solutions consist of coupled electromagnetic and plasma waves in a solitary pulse shape (Phys. Rev. Lett. 68, 3172(1992); Phys. Plasmas 9, 1820(2002)).Issues pertaining to their stability, mutual collisional interactions and propagation in an inhomogeneous plasma medium are addressed. It is found that solitary pulses that consist of a single light peak trapped in a modulated density structure are long lived whereas structures with multiple peaks of trapped light develop an instability at the trailing edge. The interaction properties of two single peak structures show interesting dependencies on their relative amplitudes and propagation speeds and can be understood in terms of their propagation characteristics in an inhomogeneous plasma medium

Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method

We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.Comment: 11 pages, 5 figures, submitted to Phys. Rev.