Specific Features of the Self-Action Dynamics of Wave Packets with Initially Normal Group-Velocity Dispersion in Nonlinear Lattices

Specific features of the self-action of wave fields are studied in the framework of a discrete nonlinear Schrödinger equation (DNSE). It is shown analytically and numerically that the dynamics of wave packets with initially normal group-velocity dispersion in systems described by this model equation may differ significantly from the evolution of similar distributions in a continuous medium. The behavior of wave fields with initially smooth (compared to the lattice period) amplitude profile and phase front is analyzed in detail, and the mechanism of their destruction in chains of equidistant elements is studied. A modification of the dispersionless approximation is proposed, which makes it possible to theoretically describe the effects leading to the development of small-scale instabilities against the background of a smooth envelope and to its subsequent significant deformations (up to destruction). Estimates of critical parameters are presented above which one should expect the above-mentioned processes (uncharacteristic of continuous media).