Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations

Details Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations

2004-06-15

arxiv.org/abs/nlin/0406029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages

Scientific paper

10.1016/j.physd.2004.06.007

We 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 {\it Ansatz} to derive the equations of motion of the collective coordinates (CCs) for the perturbed sine-Gordon (sG) and $\phi^{4}$ systems. For the $N$ collective coordinates, regardless of the {\it Ansatz} used, we show that, for the nonlinear Klein-Gordon equations, this approach is equivalent to the {\it Generalized Traveling Wave Ansatz} ({\it GTWA})

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