Article

Pramana

, Volume 79, Issue 3, pp 377-392

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

  • Avinash KhareAffiliated withIndian Institute of Science Education and Research, Raja Ramanna Fellow
  • , Avadh SaxenaAffiliated withTheoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory Email author 
  • , Apoorva KhareAffiliated withDepartments of Mathematics and Statistics, Stanford University

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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.

Keywords

Solitons Jacobi elliptic functions field theories phase transitions

PACS Nos

11.10.Lm 05.45.Yv 02.30.Gp