Modulational stability brought by cubic-quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential

This work extends to higher-order interactions the results of Nguetcho (2017), 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 an extended nonlinear Schrodinger equation (eNLS) containing a new higher-order nonlinear term. By employing linear stability analysis, the generic properties of the MI gain spectra of the system are demonstrated. In the presence of the new quartic nonlinearity, the combinations of the system's parameters open a large variety of gain profiles and instability domains that cannot be explored without the quartic nonlinearity. Direct numerical simulations are performed to support our analytical results, and an excellent agreement is found. (C) 2021 Elsevier B.V. All rights reserved.