Abstract
The continuous nonlinear Schrödinger equation has both nonintegrable and integrable discretizations. In this paper we consider the question of whether these discretizations are equivalent as models for modulated waves on nonlinear lattices. The evolution equations for the envelope of discrete modulated waves on the sine-Gordon lattice are derived by the method of multiple scales. Both the standard discrete nonlinear Schrödinger equation and its integrable variant are obtained. The integrable variant is not generic.
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© 1993 Springer Science+Business Media New York
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Rose, M. (1993). Discrete Modulated Waves. In: Christiansen, P.L., Eilbeck, J.C., Parmentier, R.D. (eds) Future Directions of Nonlinear Dynamics in Physical and Biological Systems. NATO ASI Series, vol 312. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1609-9_44
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DOI: https://doi.org/10.1007/978-1-4899-1609-9_44
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