Pramana

, Volume 79, Issue 3, pp 377–392

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

Article

DOI: 10.1007/s12043-012-0327-0

Cite this article as:
Khare, A., Saxena, A. & Khare, A. Pramana - J Phys (2012) 79: 377. doi:10.1007/s12043-012-0327-0

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 ϕ4 model and (iv) coupled ϕ6 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

SolitonsJacobi elliptic functionsfield theoriesphase transitions

PACS Nos

11.10.Lm05.45.Yv02.30.Gp

Copyright information

© Indian Academy of Sciences 2012

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research, Raja Ramanna FellowPuneIndia
  2. 2.Theoretical Division and Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  3. 3.Departments of Mathematics and StatisticsStanford UniversityStanfordUSA