«A collective variable approach for pulse propagation in nonlinear transmission media governed by the NLS equations and derivative equations».

Abstract: In the context of nonlinear transmission media there is a multiplicity of analytical methods to study the dynamics of waves. Amongst them, one can cite the Adomians based method, the tanh and extended-tanh method function, expansion methods, coupled of integration schemes, Kudryashov methods, rational (G/G)-expansion approach, sine-Gordon equation method, Jacobi elliptic method, just to cite a few. Nevertheless, a non-Lagrangian method, namely the collective variables (CV) approach can be employed to investigate different types of nonlinear Schrödinger (NLS) and evolution equations. CV approach consists to decompose the original field into a residual field and an approximated field (ansatz) containing some parameters which describe its behavior with localized collective phenomena. Hence, it is possible to derive CV for non-integrable systems. This technique is used to study pulse propagation in nonlinear optical fibers and nonlinear transmission lines for instance.