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https://www.ias.ac.in/article/fulltext/pram/079/03/0377-0392

Solitons; Jacobi elliptic functions; field theories; phase transitions.

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 $\phi^4$ model and (iv) coupled $\phi^6$ 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.

Avinash Khare¹ Avadh Saxena² Apoorva Khare³

1. Indian Institute of Science Education and Research, Raja Ramanna Fellow, Pune 411 021, India
2. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3. Departments of Mathematics and Statistics, Stanford University, Stanford, CA 94305, USA

Published

September 2012

Manuscript received

23 January 2012

Manuscript revised

29 March 2012

Accepted

18 April 2012