Search results for "Linear system"
showing 10 items of 1558 documents
Spatial Soliton Dynamics in Two-Dimensional Quadratic Photonic Crystals
2007
We present a theoretical and experimental investigation of soliton dynamics associated to twin-beam second harmonic generation in a purely nonlinear two-dimensional planar photonic lattice in LiNbO3.
q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice
2000
We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed lattice for which in continuum limit the equations of motion become the envelope Maxwell-Bloch (or SIT) equations describing the resonant interaction of light with a nonlinear dielectric. Thus the N-soliton solutions we here report are the natural q-deformations, necessary for a lattice, of the well-known multi-soliton and breather solutions of self-induced transparency (SIT). The method we use to find these solutions is a generalization of the Darboux-Backl…
Random quasi-phase-matched second-harmonic generation in periodically poled lithium tantalate
2010
We observe second harmonic generation via random quasi-phase-matching in a 2.0 micron periodically poled, 1-cm-long, z-cut lithium tantalate. Away from resonance, the harmonic output profiles exhibit a characteristic pattern stemming from a stochastic domain distribution and a quadratic growth with the fundamental excitation, as well as a broadband spectral response. The results are in good agreement with a simple model and numerical simulations in the undepleted regime, assuming an anisotropic spread of the random nonlinear component. (C) 2010 Optical Society of America
On the wave interaction in a charged fluid with Hall and ion slip-currents
1983
The evolution of non linear small perturbations in a charged fluid with generalized Ohm's law is considered, pointing out the possibility of effects due to interaction between different waves. Following the perturbative reductive methods, some phase functions for studying interaction are introduced. A suitable hypothesis on their evolution permits us to prove that the amplitudes of the first order perturbation obey Burgers-like equations, in which the dissipative terms are not influenced by the Hall effect.
Oscillations of a highly discrete breather with a critical regime
2000
We analyze carefully the essential features of the dynamics of a stationary discrete breather in the ultimate degree of energy localization in a nonlinear Klein-Gordon lattice with an on-site double-well potential. We demonstrate the existence of three different regimes of oscillatory motion in the breather dynamics, which are closely related to the motion of the central particle in an effective potential having two nondegenerate wells. In given parameter regions, we observe an untrapped regime, in which the central particle executes large-amplitude oscillations from one to the other side of the potential barrier. In other parameter regions, we find the trapped regime, in which the central …
Anisotropic Heisenberg chain with composite spin
1986
A family of one-dimensional magnetic Hamiltonians is introduced, where at each site there are $n$ spin-$S$ operators. It is shown that, for special couplings between spins and for $S=\frac{1}{2}$, the model contains the complete spectrum of the Heisenberg chain with spins \textonehalf{}, 1, frac32;, etc., and the ground state is that of the corresponding Heisenberg chain. By the varying of a single parameter the model allows continuous transitions between chains with different spin. We map the spin-($S+S$) model onto the nonlinear $\ensuremath{\sigma}$ model and discuss the possibility of a finite gap in the spin-(\textonehalf{}+\textonehalf{}) model.
Nonlinear inverse bremsstrahlung and highly anisotropic electron distributions
1996
A procedure is proposed to deal with the approximate solution of the kinetic equation for the velocity distribution function of electrons in a fully ionized plasma in the presence of strong, high frequency radiation. The Legendre polynomial expansion is applied after the kinetic equation has been written in an oscillating frame, where some directions are appropriately scaled, with the aim of making approximately isotropic, on the average, distributions that are otherwise anisotropic. The equations are derived for the isotropic part of the electron distribution in the scaled frame and for the scaling factor. The procedure is meant to display its potential in cases where the electron distribu…
Non-adiabatic manipulation of slow-light solitons
2005
We provide an exact analytic description of decelerating, stopping and reaccelerating optical solitons in atomic media in the non-adiabatic regime. Dynamical control over slow-light pulses is realized via a nonlinear interplay between the solitons and the controlling field generated by an auxiliary laser. This leads to recovery of optical information. We discuss physically interesting features of our solution, which are in good agreement with recent experiments.
Ansatz independent solution of a soliton in a strong dispersion-management system
2001
We introduce a theoretical approach to the study of propagation in systems with periodic strongmanagement dispersion. Our approach does not assume any ansatz about the form of the solution nor does it make use of any average procedure. We find an explicit solution for the pulse evolution in the fast dynamics regime ~distances smaller than the dispersion period!. We also establish the equation of motion governing the slow dynamics of an arbitrary pulse and prove that the pulse evolution is nonlinear and Hamiltonian. We solve this equation and find that a nonlinear solitonlike solution occurs self-consistently in the form of an asymptotic stationary eigenfunction of the Hamiltonian.
COMPRESSION OF ENVELOPE SOLITONS IN NONLINEAR ELECTRICAL LINES
1989
Resume : La propagation des solitons enveloppe dans les lignes non lineaires de transmission electrique et de transmission Josephson est etudiee sous l'aspect theorique et en simulation numerique. Dans l'approximation des milieux continus et la limite des faibles amplitudes, les equations caracteristiques de ces lignes se ramenent a l'equation NLS . La solution "a deux solitons enveloppe" se propage parfaitement dans les lignes considerees avec des phenomenes de recurrence et de compression d'enveloppe. Ceci est observe egalement pour des profils d'excitation non solution de NLS, ce qui est d'un grand interet pour les applications pratiques.