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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.

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Authors and Affiliations

  1. Indian Institute of Science Education and Research, Raja Ramanna Fellow, Pune, 411 021, India

    Avinash Khare

  2. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Avadh Saxena

  3. Departments of Mathematics and Statistics, Stanford University, Stanford, CA, 94305, USA

    Apoorva Khare

Authors
  1. Avinash Khare
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  2. Avadh Saxena
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  3. Apoorva Khare
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Correspondence to Avadh Saxena.

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Khare, A., Saxena, A. & Khare, A. Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order. Pramana - J Phys 79, 377–392 (2012). https://doi.org/10.1007/s12043-012-0327-0

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  • DOI: https://doi.org/10.1007/s12043-012-0327-0

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