Backlund Transformation and Quasi-Integrable Deformation of Mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models

DOI10.5890/DNC.2018.03.003zbMATH Open1396.37077arXiv1701.01929WikidataQ129996916 ScholiaQ129996916MaRDI QIDQ4682678

Kumar Abhinav, Partha Guha, A. Ghose Choudhury

Publication date: 18 September 2018

Published in: The interdisciplinary journal of Discontinuity, Complexity, and Nonlinearity (Search for Journal in Brave)

Abstract: In this paper we study a non-linear partial differential equation (PDE), proposed by N. Kudryashov [arXiv:1611.06813v1[nlin.SI]], using continuum limit approximation of mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models. This generalized semi-discrete equation can be considered as a model for the description of non-linear dislocation waves in crystal lattice and the corresponding continuous system can be called mixed generalized potential KdV and sine-Gordon equation. We obtain the B"acklund transformation of this equation in Riccati form in inverse method. We further study the quasi-integrable deformation of this model.

Full work available at URL: https://arxiv.org/abs/1701.01929

zbMATH Keywords

Bäcklund transformationFrenkel-Kontorova modelFermi-Pasta-Ulam equationquasi-integrable deformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Lattice dynamics; integrable lattice equations (37K60)

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