Optical soliton perturbation and polarization with quadratic--cubic nonlinearity by sine-Gordon equation approach

Soliton evolution and radiation loss for the sine-Gordon equation.

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parame...

Towards soliton solutions of a perturbed sine-Gordon equation

We give arguments for the existence of exact travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. Such solutions are allowed exactly by the energy balance of these terms, and can be observed experimentally e....

, mKdV , SINE - GORDON SOLITON EQUATIONS

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

Perturbation analysis of a parametrically changed sine-Gordon equation.

Perturbation Theory for the Double–Sine–Gordon Equation

This paper presents the perturbation theory for the double–sine–Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation’s influence. In particular case λ = 0 the results of the research transform into well-known perturbation theory for the sine–Gordon equation.