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.