Lagrangian formalism in perturbed nonlinear Klein-Gordon equations

PHYSICA D-NONLINEAR PHENOMENA

卷:197

Article

Quintero, NR ; Zamora-Sillero, E

关键词: collective coordinates;    solitons;    solitary waves;    perturbed nonlinear Klein-Gordon equations;   

DOI  :  10.1016/j.physd.2004.06.007

来源: Elsevier

【 摘 要 】

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 Laarangian 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 (M) for the perturbed sine-Gordon (sG) and phi(4) 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 (GTMA). (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free