Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

TL;DR

This paper analytically investigates asymmetric gap soliton modes and intrinsic localized modes in one-dimensional diatomic lattices with cubic and quartic nonlinearities, providing explicit criteria and expressions for their occurrence.

Contribution

It introduces explicit analytical criteria and expressions for asymmetric gap solitons and localized modes in diatomic lattices with complex nonlinearities, extending previous numerical studies.

Findings

Explicit criteria for asymmetric gap solitons and localized modes.

Analytical expressions for particle displacements of localized excitations.

Good agreement with previous numerical results for standard potentials.

Abstract

Nonlinear localized excitations in one-dimensional diatomic lattices with cubic and quartic nonlinearity are considered analytically by a quasi-discreteness approach. The criteria for the occurence of asymmetric gap solitons (with vibrating frequency lying in the gap of phonon bands) and small-amplitude, asymmetric intrinsic localized modes (with the vibrating frequency being above all the phonon bands) are obtained explicitly based on the modulational instabilities of corresponding linear lattice plane waves. The expressions of particle displacement for all these nonlinear localized excitations are also given. The result is applied to standard two-body potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The comparison with previous numerical study of the anharmonic gap modes in diatomic lattices for the standard two-body potentials is made and good agreement is found.