Skip to main content
Breathers for the Discrete Nonlinear Schrödinger equation with nonlinear hopping
Journal of Nonlinear Science (2012)
  • N. I. Karachalios
  • B. Sánchez-Rey
  • Panos Kevrekidis
  • J. Cuevas
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below the prescribed lower bounds of the power which depend on the dimension, the parameters of the lattice as well as of the frequency of breathers. In the case of supercritical power nonlinearities we investigate the interplay of these estimates with the optimal constant of the discrete interpolation inequality. Improvements of the general estimates, taking into account the localization of the true breather solutions are derived. Numerical studies in the one dimensional lattice corroborate the theoretical bounds and illustrate that in certain parameter regimes of physical significance, the estimates can serve as accurate predictors of the breather power and its dependence on the various system parameters.
Publication Date
Publisher Statement
This is the pre-published version harvested from arXiv. The published version is located at
Citation Information
N. I. Karachalios, B. Sánchez-Rey, Panos Kevrekidis and J. Cuevas. "Breathers for the Discrete Nonlinear Schrödinger equation with nonlinear hopping" Journal of Nonlinear Science (2012)
Available at: