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Length scale competition in nonlinear Klein-Gordon models: a collective coordinate approach
1Grupo Interdisciplinar de Sistemas Complejos (GISC) and Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain. scuenda@math.uc3m.es
Chaos (Woodbury, N.Y.)
|July 23, 2005
Summary
Length scale competition in nonlinear Klein-Gordon models is explained using a collective coordinate approach. This method simplifies understanding soliton instabilities and can be applied to various nonlinear models.
Area of Science:
- Nonlinear dynamics
- Soliton physics
- Mathematical physics
Background:
- Solitons are stable, localized waves in nonlinear systems.
- Length scale competition is an instability affecting solitons under specific perturbations.
- Previous explanations of this phenomenon were complex.
Purpose of the Study:
- To provide a simpler explanation for length scale competition in solitons.
- To introduce a collective coordinate approach for analyzing soliton instabilities.
- To extend the analysis to a broader range of nonlinear models.
Main Methods:
- Utilized nonlinear Klein-Gordon models as a case study.
- Employed a collective coordinate approach focusing on soliton position and width.
- Analyzed the dynamics of solitons under length-specific perturbations.
Main Results:
- Demonstrated that length scale competition can be understood through soliton position and width dynamics.
- Developed a simplified framework for explaining this soliton instability.
- Showcased the applicability of the collective coordinate method to various soliton-bearing models.
Conclusions:
- The collective coordinate approach offers a natural and simplified explanation for length scale competition.
- This technique is broadly applicable to diverse nonlinear models and coherent structures.
- The study enhances the understanding of soliton behavior in nonlinear systems.