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Working within the framework of nonlinear Klein–Gordon models as a paradigmatic example, we show that length scale competition, an instability of solitons subjected to perturbations of an specific length, can be understood by means of a collective coordinate approach in terms of soliton position and width. As a consequence, we provide a natural explanation of the phenomenon in much simpler terms than any previous treatment of the problem. Our technique allows us 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.

Solitons, solitary waves, vortices, and other coherent structures possess, generally speaking, a characteristic length or size. One important feature of these coherent structures, which usually are exact solutions of certain nonlinear models, is their robustness when the corresponding …