Effects of nonlinearity and substrate’s deformability on modulation instability in NKG equation
International audience; This article investigates combined effects of nonlinearities and substrate's deformability on modulational instability. For that, we consider a lattice model based on the nonlinear Klein-Gordon equation with an on-site potential of deformable shape. Such a consideration enables to broaden the description of energy-localization mechanisms in various physical systems. We consider the strong-coupling limit and employ semi-discrete approximation to show that nonlinear wave modulations can be described by an extended nonlinear Schrodinger equation containing a fourth-order dispersion component. The stability of modulation of carrier waves is scrutinized and the following …
Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential
Abstract This work extends to higher-order interactions the results of Ref. Nguetcho (2021), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic-quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel-Kontorova model, is …