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Rapti, Z., Kevrekidis, P.G., Smerzi, A. and Bishop, A.R. (2004) Parametric and Modulational Instabilities of the Discrete Nonlinear Schrodinger Equation. Journal of Physics B: Atomic, Molecular and Optical Physics, 37, 1481-1514. https://doi.org/10.1088/0953-4075/37/7/070

has been cited by the following article:

• TITLE: Arnold Tongues for Discrete Hill’s Equation

  AUTHORS: José Guillermo Rodríguez Servín, M. Joaquin Collado

  KEYWORDS: Arnold Tongues, Discrete Hill’s Equation, Monodromy Matrix, Discretized Hamiltonian

  JOURNAL NAME: Applied Mathematics, Vol.8 No.12, December 29, 2017

  ABSTRACT: In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called Discretized Hill’s equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill’s equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill’s equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.