Search results for "sine-Gordon equation"
showing 4 items of 4 documents
Analytical investigation of solitary waves in nonlinear Kerr medium
2004
Abstract We study analytically the solution of nonlinear equation which result from the propagation of electromagnetic waves within a nonlinear Kerr medium. The medium is characterized by a dielectric constant which varies periodically and depends on the local field intensity. As a first step, we detail the resolution of the nonlinear equations with a quadratic nonlinearity. After that, we apply the slowly varying envelope approximation to obtain a Sine–Gordon equation. In this kind of nonlinearity, a gap solitons occurs. Moreover we verify that the solutions of the nonlinear equation for all frequencies within the gap are solitons solutions. After that we study the conditions of apparition…
Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method
1990
Abstract Using the classical action-angle variables for the continuous model, we study the thermodynamics of the classical Heisenberg chain in an applied field by a generalized Bethe ansatz approach. The crucial point consists in the derivation of a phase-shifted density of states for the excitations of the model, obtained by imposing periodic boundary conditions. In the thermodynamic limit, the free energy can be expressed in terms of the solution of a non-linear integral equation, showing the universal dependece of the variable x=(JH) 1 2 /T .
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.
Impurity effects on soliton dynamics in planar ferromagnets
1993
Abstract We investigate numerically the dynamics of solitons in a ferromagnetic spin chain and we show that the sine-Gordon approximation provides only a poor description of the solitary excitations in the presence of impurities. Depending on their energy and the strength of the impurity, solitons can be reflected or transmitted. When they are reflected, they can suffer abrupt changes in velocity, which are associated to the switch from one soliton branch to another. In some cases the scattering by an impurity can excite an internal mode of the soliton, which is able to store some energy and modify the output of the scattering.