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Discontinuity, Nonlinearity, and Complexity 7(1) (2018) 31--41 | DOI:10.5890/DNC.2018.03.003

Kumar Abhinav$^{1}$, A Ghose Choudhury$^{2}$, Partha Guha$^{1}$

$^{1}$ SN Bose National Centre for Basic Sciences JD Block, Sector III, Salt Lake, Kolkata 700106, India

$^{2}$ Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta 700009, India

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Abstract

In this paper we study a non-linear partial differential equation (PDE), proposed by 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 Bäcklund transformation of this equation in Riccati form in inverse method. We further study the quasi-integrable deformation of this model.

Acknowledgments

The authors are grateful to Professors Luiz. A. Ferreira, Wojtek J. Zakrzewski and Betti Hartmann for their encouragement, various useful discussions and critical reading of the draft. This paper is dedicated to the memory of our friend Anjan Kundu, his death cut short a productive career.

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