Localization in the Liouville Lattice and Movable Discrete Breathers.

Nonlinear differential-difference equations (nonlinear lattices) exhibit single soliton solutions in the form of 1-breathers. These solutions are time-periodic and exponentially localized in space. Necessary condition for their existence is the upper bounds on the linear spectrum of small perturbations around stationary point of the system. Unlike continuous models, integrability property do not help nonlinear lattices to have multi-breather solutions. The C-integrable Liouville lattice is discussed in view to get moving breathers, i.e. true time-periodic multi-solitons with free velocity and amplitude. We construct analogs of instanton solutions which are localized both in space and time. [ABSTRACT FROM AUTHOR]