Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations
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, calcul...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42716 |
| Acceso en línea: | http://hdl.handle.net/11441/42716 https://doi.org/10.1016/j.physd.2004.06.007 |
| Access Level: | acceso abierto |
| Palabra clave: | Collective coordinates Solitary waves Perturbed Nonlinear Klein-Gordon equations |
| Sumario: | 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 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). |
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