Quintero, Niurka R.Zamora-Sillero, Elías2016-06-242016-06-242004Quintero, N.R. y Zamora-Sillero, E. (2004). Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations. Physica D, 197, 1-9.0167-2789http://hdl.handle.net/11441/42716We develop an alternative approach to study the effect of the generic perturbation (in addition to explicitly considering the loss term) in the nonlinear Klein–Gordon equations. By a change of the variables that cancel the dissipation term we are able to write the Lagrangian density and then, calculate the Lagrangian as a function of collective variables. We use the Lagrangian formalism together with the Rice Ansatz to derive the equations of motion of the collective coordinates (CCs) for the perturbed sine-Gordon (sG) and φ4 systems. For the N collective coordinates, regardless of the Ansatz used, we show that, for the nonlinear Klein–Gordon equations, this approach is equivalent to the Generalized Traveling Wave Ansatz (GTWA).application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Collective coordinatesSolitary wavesPerturbed Nonlinear Klein-Gordon equationsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.physd.2004.06.007