Length scale competition in soliton bearing equations: A collective coordinate approach

Abstract

We study the phenomenon of length scale competition, an instability of solitons and other coherent structures that takes place when their size is of the same order of some characteristic scale of the system in which they propagate. Working on the framework of nonlinear Klein-Gordon models as a paradigmatic example, we show that this instability can be understood by means of a collective coordinate approach in terms of soliton position and width. As a consequence, we provide a quantitative, natural explanation of the phenomenon in much simpler terms than any previous treatment of the problem. Our technique allows to study the existence of length scale competition in most soliton bearing nonlinear models and can be extended to coherent structures with more degrees of freedom, such as breathers.

arXiv comment5 pages, 3 figures

References in corpus (7)

• Interaction of sine-Gordon kinks with defects: The two-bounce resonance
• Internal mode mechanism for collective energy transport in extended systems
• Resonances in the dynamics of ${\varphi }^4$ kinks perturbed by ac forces
• Anomalous resonance phenomena of solitary waves with internal modes
• On the existence of internal modes of sine-Gordon kinks
• Kink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation
• Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations

Cited by in corpus (3)

• Effective Particle Methods for Fisher-Kolmogorov Equations: Theory and Applications to Brain Tumor Dynamics
• Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity
• Domain wall dynamics in expanding spaces