Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Localized solutions of a nonlinear diatomic lattice

Authors: V. V. Konotop and G. Perla Menzala
Journal: Quart. Appl. Math. 63 (2005), 201-223
MSC (2000): Primary 39A10, 39B72
DOI: https://doi.org/10.1090/S0033-569X-05-00952-6
Published electronically: February 18, 2005
MathSciNet review: 2150770
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Abstract: We consider a coupled system of differential-difference nonlinear equations. We study the dynamics of such a diatomic lattice showing global existence and uniqueness in an appropriate function space. Our approach based on energy estimates allows us to prove the result only in the case where nonlinear force constants are positive and equal. All other situations remain at this point as open problems.

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V. V. Konotop
Affiliation: Centro de Física Teórica e Computacional, Universidade de Lisboa, Complexo Interdisciplinar, Av. Professor Gama Pinto 2, 1649-003 Lisbon, Portugal
Email: konotop@cii.fc.ul.pt

G. Perla Menzala
Affiliation: National Laboratory of Scientific Computation, LNCC/MCT, Rua Getulio Vargas 333, Petropolis, RJ, CEP 25651-070, Brasil and Federal University of Rio de Janeiro, Institute of Mathematics, P.O. Box 68530, 21945-970, Rio de Janeiro, RJ, Brasil
Email: perla@lncc.br

DOI: https://doi.org/10.1090/S0033-569X-05-00952-6
Keywords: Nonlinear lattices, high interaction, diatomic case
Received by editor(s): March 1, 2003
Published electronically: February 18, 2005
Article copyright: © Copyright 2005 Brown University

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