Search results for "Nonlinear system"
showing 10 items of 1446 documents
Solitons and modulational instability
1996
We introduce the localized nonlinear waves called solitons which can occur in nature with different profiles such as kink, pulse, and envelope solitons. The envelope-soliton is important because without modulation the wave carry no information. It is a solution of the so-called nonlinear Schrodinger equation which describes the evolution of dispersive and weakly nonlinear waves. The generation of envelope soliton trains can result from the modulational instability phenomenon that leads to self induced modulations, with respect to small perturbations, such as noise, of input plane wave.
Nonlinear Schrödinger models and modulational instability in real electrical lattices
1995
International audience; In nonlinear dispersive media, the propagation of modulated waves, such as envelope (bright) solitons or hole (dark) solitons, has been the subject of considerable interest for many years, as for example in nonlinear optics [A.C. Newell and J.V. Moloney, Nonlinear Optics (Addison-Presley, 1991)]. On the other hand, discrete electrical transmission lines are very convenient tools to study the wave propagation in 1D nonlinear dispersive media [A.C. Scott (Wiley-Interscience, 1970)]. In the present paper, we study the generation of nonlinear modulated waves in real electrical lattices. In the continuum limit, our theoretical analysis based on the Nonlinear Schrodinger e…
Classical and Quantum Nonultralocal Systems on the Lattice
1997
We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.
Polarization Domain Wall Solitons with Counterpropagating Laser Beams
1998
The coupling between two intense laser beams in a nonlinear dielectric leads to a host of physical effects. In particular, the interaction between the polarization states of two counterpropagating ligth beams may generate polarization domain wall (PDW7) solitons [1]. We present what we believe is the first experimental observation of PDW7 soliton formation in a nonlinear dielectric medium.
On the application of canonical perturbation theory to floppy molecules
2000
International audience; Canonical perturbation theory (CPT) is a powerful tool in the field of molecular physics. It consists of a series of coordinate transformations aimed at rewriting the Hamiltonian in a simpler form without modifying the geometry of the phase space. The major achievement of CPT is the straightforward derivation of relations between the physically meaningful parameters of potential energy surfaces and the coefficients of the so-called effective Hamiltonians. While most of the studies performed up to date deal with surfaces expanded in polynomial series around a single minimum, CPT has also been applied to mixed polynomial/trigonometric expansions in the treatment of tor…
A Temperature Dependent Non-Linear Inductor Model for a DC/DC Boost Converter
2018
This paper is focused on the use of non-linear inductors in DC/DC switching converters, as well as their behaviour due to changes in current and temperature. The model of an inductor is set up on the basis of experimental data, which are automatically acquired by a virtual instrument; from those data, a polynomial curve describing the inductance variations is obtained. The analysis of the converter, performed by including the proposed model, is validated by experimental tests.
A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two
2008
Abstract We suggest how one can obtain exact solutions of some type of coupled Korteweg–de Vries equations by means of hyperelliptic functions of genus two.
Dynamics of breather modes in a nonlinear “helicoidal” model of DNA
1991
Via a recent model with an additional helicoidal coupling, the dynamics of breathers modes in DNA are studied analytically and with the use of numerical simulations. It is shown that these excitations are longlived and can match experimentally observed fluctuational openings.
Nonlinear optical Galton board
2007
We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. {[}Phys. Rev. A \textbf{61}, 013410 (2000)], by introducing the possibility of nonlinear self--phase modulation on the wavefunction during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau--Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of non-dispersive pulses in the field distribution (soliton--like structures). These exhibit a variety…
Theory of slow-light solitons
2005
In the framework of the nonlinear $\Lambda$-model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the $\Lambda$-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the $\Lambda$-type media. We provide an exact analytic description of decelerating, stopping and re-accelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field generated by an auxiliary laser. For a rather general time dependence of the fiel…