Breathers for the Discrete Nonlinear Schrödinger Equation with Nonlinear Hopping
نویسندگان
چکیده
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schrödinger 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. Communicated by P. Newton. N.I. Karachalios ( ) Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece e-mail: [email protected] B. Sánchez-Rey · J. Cuevas Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, C/Virgen de Africa, 7, 41011 Sevilla, Spain P.G. Kevrekidis Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003-9305, USA 206 J Nonlinear Sci (2013) 23:205–239
منابع مشابه
Erratum to: Breathers for the Discrete Nonlinear Schrödinger Equation with Nonlinear Hopping
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عنوان ژورنال:
- J. Nonlinear Science
دوره 23 شماره
صفحات -
تاریخ انتشار 2013