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A Discrete Nonlinear Model With Substrate Feedback, Panos Kevrekidis, B. A. Malomed, A. R. Bishop
A Discrete Nonlinear Model With Substrate Feedback, Panos Kevrekidis, B. A. Malomed, A. R. Bishop
Panos Kevrekidis
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial …
Discrete Nonlinear Model With Substrate Feedback, P. G. Kevrekidis, B. A. Malomed, A. R. Bishop
Discrete Nonlinear Model With Substrate Feedback, P. G. Kevrekidis, B. A. Malomed, A. R. Bishop
Panos Kevrekidis
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial …