Search results for "Integrable system"
showing 10 items of 354 documents
Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics
2006
Abstract Taking into account many developments in fiber optics communications, we propose a higher nonlinear Schrodinger equation (HNLS) with variable coefficients, more general than that in [R. Essiambre, G.P. Agrawal, Opt. Commun. 131 (1996) 274], which governs the propagation of ultrashort pulses in a fiber optics with generic variable dispersion. The study of this equation is performed using the Painleve test and the zero-curvature method. Also, we prove the equivalence between this equation and its anomalous integrable counterpart (the so-called Sasa–Satsuma equation). Finally, in view of its physical relevance, we present a soliton solution which represents the propagation of ultrasho…
Stable coupled conjugate solitary waves in optical fibers.
1998
Four-wave mixing of an intense continuous-wave pump beam with an ultrashort soliton signal in an optical fiber is theoretically analyzed. A novel class of stable two-color coupled solitary waves is found. These vector parametric solitons represent the optimal frequency conversion of an ultrashort pulse. © 1998 Optical Society of America.
Non-existence of dark solitons in a nonlinear Schrödinger-Maxwell-Bloch fibre system
2000
We consider the coupled system of nonlinear Schrodinger and Maxwell-Bloch (NLS-MB) equations, which govern the nonlinear pulse propagation in erbium doped optical fibres. With the help of the Painleve singularity structure analysis, we prove the non-existence of optical solitons in the NLS-MB fibre system in the normal dispersion regime.
Exact dark soliton solutions for a family ofNcoupled nonlinear Schrödinger equations in optical fiber media
2001
We consider a family of N coupled nonlinear Schr\"odinger equations which govern the simultaneous propagation of N fields in the normal dispersion regime of an optical fiber with various important physical effects. The linear eigenvalue problem associated with the integrable form of all the equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.
Determination of the top quark mass circa 2013: methods, subtleties, perspectives
2013
We present an up-to-date overview of the problem of top quark mass determination. We assess the need for precision in the top mass extraction in the LHC era together with the main theoretical and experimental issues arising in precision top mass determination. We collect and document existing results on top mass determination at hadron colliders and map the prospects for future precision top mass determination at e+e- colliders. We present a collection of estimates for the ultimate precision of various methods for top quark mass extraction at the LHC.
Statistical mechanics of the NLS models and their avatars
2006
“In Vishnuland what avatar? Or who in Moscow (Leningrad) towards the czar [1]”. The different manifestations (avatars) of the Nonlinear Schrodinger equation (NLS models) are described including both classical and quantum integrable cases. For reasons explained the sinh-Gordon and sine-Gordon models, which can be interpreted as covariant manifestations of the ‘repulsive’ and ‘attractive’ NLS models, respectively, are chosen as generic models for the statistical mechanics. It is shown in the text how the quantum and classical free energies can be calculated by a method of functional integration which uses the classical action-angle variables on the real line with decaying boundary conditions,…
Soliton rains in a fiber laser: An experimental study
2010
Rains of solitons constitute a class of nonlinear dynamics of dissipative soliton ensembles that we briefly reported in Opt. Express 17, 11776 (2009) from a fiber laser experiment. The existence of a relatively intense noisy background together with several tens of soliton pulses aggregated in a condensed soliton phase constitutes a necessary condition for their appearance. New soliton pulses form spontaneously from the background fluctuations and drift until they reach the condensed soliton phase. We here relate in detail the experimental conditions under which soliton rains manifest and their key features, describe related dynamics observed in their vicinity, and propose an explanation fo…
Classical Chern–Simons Mechanics
2001
We are interested in a completely integrable Hamiltonian system \((\mathscr{M}_{2N},\omega,H).\) Local coordinates on the 2N-dimensional phase space \(\mathscr{M}_{2N}\) are denoted by η a = (p, q), a = 1, 2, … 2N and the symplectic 2-form ω is given by
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.
On the Leibniz bracket, the Schouten bracket and the Laplacian
2003
International audience; The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.