Pramana

, Volume 79, Issue 3, pp 377–392

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

Authors

  • Avinash Khare
    • Indian Institute of Science Education and Research, Raja Ramanna Fellow
    • Theoretical Division and Center for Nonlinear StudiesLos Alamos National Laboratory
  • Apoorva Khare
    • Departments of Mathematics and StatisticsStanford University
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 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

Copyright information

© Indian Academy of Sciences 2012