Search results for "Integrable system"
showing 10 items of 354 documents
Quantized separations of phase-locked soliton pairs in fiber lasers
2003
Quantized separations of phase-locked soliton pairs in fiber lasers were presented. The relation between the Kelly sidebands and the quantized separations between solitons was confirmed. Simulation results showed that the solitons can see each other at relatively larger distances than they would in the absence of radiation.
Propagation, Stability and Interactions of Novel Three-Wave Parametric Solitons
2006
International audience; We found a new class of analytic soliton solutions that describe the parametric wave mixing of optical pulses in quadratic nonlinear crystals. We analyze the stability properties, interactions and collisions of these solitons.
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…
Statistical Mechanics of the Sine-Gordon Equation
1986
We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.
Some evolution equations arising in physics
1983
In this paper we consider a new series of evolution equations generalizing the Korteweg-deVries (KdV) and Burgers equations, and we report recent advances on these equations together with the physical phenomena where they arise. In particular we consider a generalized Burgers' equation and we sketch a method for solution in series by using the theory of Sobolevskij and Tanabe. Then we study the KdV equation with nonuniformity terms and we describe various physical interpretation of this equation. We consider various particular cases in which varying solitonic solutions exist. Also we sketch a unicity theorem. Finally modified Burgers-KdV equations are considered.
Energy-exchange collision of the Manakov vector solitons under strong environmental perturbations
2007
International audience; We use a collective-variable approach to study the dynamical behavior of vector solitons in the Manakov system under strong environmental perturbations induced by the fiber losses and a modified cross-phase modulation parameter. We identify and discuss the salient features associated with energy-exchange collisions of transmissional and reflectional types. Particularly, we find that such perturbations can induce important effects not only on fundamental soliton parameters such as the peak power, central position, width, chirp, and frequency, but also on the nature of the collision. Interestingly, we find that the perturbations lead to only a slight alteration of coll…
Efficient control of the energy exchange due to the Manakov vector-soliton collision
2003
By examining the concept of energy exchange among the orthogonally polarized components of each of two colliding (Manakov-like) vector solitons it is observed that a maximum or an efficient energy-exchange process is possible only for an appropriate choice of the initial physical parameters (namely, frequency separation, polarizations, time delay, and pulse-width separation between the colliding solitons) for which L(W) (walk-off length) >>L(NL) (nonlinear length). However, in this case only, the amount of energy-exchange can be considerably increased or decreased by appropriately changing the phases of colliding solitons without altering the walk-off length and the initial energy distribut…
A Look at Some Remarkable Mathematical Techniques
1996
The nonlinear equations that we have encountered in the previous chapters can be solved by using mathematical techniques such as the powerful inverse scattering transform (IST) (Gardner et al. 1967) and the remarkable Hirota method (Hirota 1971). Specifically, in addition to the one-soliton solutions, explicit multisoliton solutions representing the interaction of any number of solitons can be constructed. Moreover, in several cases a precise prediction, closely related to experiments, can be made by the IST of the nonlinear response of the physical system, that is, of the number of solitons that can emerge from a finite initial disturbance (Zakharov, 1980. Ablowitz and Segur 1981; Calogero…
Long-Range interaction of temporal incoherent solitons
2014
Contrary to conventional solitons, temporal incoherent solitons are sustained by a defocusing nonlinearity with anomalous dispersion and exhibit a non-mutual attractive-repulsive interaction. We explain these results by a long-range Vlasov formalism.
Breather compactons in nonlinear Klein-Gordon systems
1999
We demonstrate the existence of a localized breathing mode with a compact support, i.e., a stationary breather compacton, in a nonlinear Klein-Gordon system. This breather compacton results from a delicate balance between the harmonicity of the substrate potential and the total nonlinearity induced by the substrate potential and the coupling forces between adjacent lattice sites.