Multitransition solutions for a generalized Frenkel-Kontorova model
Wen-Long Li, Xiaojun Cui
TL;DR
This paper develops new homoclinic and heteroclinic solutions for a generalized Frenkel-Kontorova model using minimal and Birkhoff solutions as building blocks, employing constrained minimization techniques.
Contribution
It introduces a method to construct non-minimal, non-Birkhoff solutions in a generalized Frenkel-Kontorova model under gap conditions.
Findings
Constructed numerous homoclinic solutions
Constructed heteroclinic solutions
Used constrained minimization method
Abstract
We study a generalized Frenkel-Kontorova model. Using minimal and Birkhoff solutions as building blocks, we construct a lot of homoclinic solutions and heteroclinic solutions for this generalized Frenkel-Kontorova model under gap conditions. These new solutions are not minimal and Birkhoff any more. We use constrained minimization method to prove our results.
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Taxonomy
TopicsNonlinear Waves and Solitons · Mathematical and Theoretical Epidemiology and Ecology Models · Differential Equations and Numerical Methods