Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss applications of the discrete nonlinear Schrodinger equation in the context of existence and stability of breathers of the Klein--Gordon lattice.

Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrodinger equations / P. D., T. Penati, S. Paleari. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - 28:7(2016 Aug 31). [10.1142/S0129055X1650015X]

Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrodinger equations

T. Penati
Secondo
;
S. Paleari
Ultimo
2016

Abstract

Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss applications of the discrete nonlinear Schrodinger equation in the context of existence and stability of breathers of the Klein--Gordon lattice.
Klein–Gordon lattice; discrete nonlinear Schr¨odinger equations; existence and stability of breathers; small-amplitude approximations; energy method; normal forms
Settore MAT/07 - Fisica Matematica
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/429864
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