Abstract
Exact anharmonic-localized-mode solutions to the discrete nonlinear Schrödinger (NLS) equation defined in a d-dimensional version of the simple cubic lattice are obtained in terms of lattice Green’s functions described by the ordinary and modified Bessel functions. A stationary or nonmoving localized mode is shown to be stable, while a moving one disperses, the rate of dispersing being smaller for a smaller moving velocity. For d≥3 there exists a critical value of the lattice nonlinearity for the appearance of such a localized mode, and its spatial localization becomes pronounced as d increases. For d=1 the solution reduces in the continuum limit to the conventional one-soliton solution of the NLS equation. A very brief study is also made on the two-localized-mode problem.
