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arXiv · 1701.01929

B\"acklund Transformation and Quasi-Integrable Deformation of Mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models

Kumar Abhinav·A Ghose Choudhury·Partha Guha
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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.

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Kumar Abhinav, A Ghose Choudhury, Partha Guha. 2017-01-08. B\"acklund Transformation and Quasi-Integrable Deformation of Mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models. https://doi.org/10.5890/dnc.2018.3.003

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