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Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order |
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| Authors: | Avinash Khare Avadh Saxena Apoorva Khare |
| Institution: | 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 |
| 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?CLadik model, (iii) coupled ? 4 model and (iv) coupled ? 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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