, Volume 79, Issue 3, pp 377-392
Date: 16 Aug 2012

Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order

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Abstract

Coupled discrete models are ubiquitous in a variety of physical contexts. We provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lamé polynomials of arbitrary order. The models discussed are: (i) coupled Salerno model, (ii) coupled Ablowitz–Ladik model, (iii) coupled ϕ 4 model and (iv) coupled ϕ 6 model. In all these cases we show that the coefficients of the Lamé polynomials are such that the Lamé polynomials can be re-expressed in terms of Chebyshev polynomials of the relevant Jacobi elliptic function.