C. Chong, D.E. Pelinovsky, and G. Schneider

On the validity of the variational approximation in discrete nonlinear Schrodinger equations

Physica D 241, 115-124 (2012)

The variational approximation is a well known tool to approximate localized states in Hamiltonian systems. In the context of a discrete nonlinear Schrodinger equation with a small coupling constant, we prove error estimates for the variational approximations of site-symmetric, bond-symmetric, and the twisted discrete solitons. This is shown for various trial configurations, which become increasingly more accurate as more parameters are taken. It is also shown that the variational approximation yields the correct spectral stability result and control oscillatory dynamics of stable discrete solitons for long but finite time intervals.

Discrete nonlinear Schrodinger equations, Existence and stability of discrete solitons, Justification of variational approximations.