  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.
