Cyclic identities for Jacobi elliptic and related functions

Khare, Avinash ; Lakshminarayan, Arul ; Sukhatme, Uday (2003) Cyclic identities for Jacobi elliptic and related functions Journal of Mathematical Physics, 44 (4). pp. 1822-1841. ISSN 0022-2488

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Official URL: http://jmp.aip.org/resource/1/jmapaq/v44/i4/p1822_...

Related URL: http://dx.doi.org/10.1063/1.1560856

Abstract

Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at p equally shifted points on the real axis were recently found. These identities played a crucial role in discovering linear superposition solutions of a large number of important nonlinear equations. We derive four master identities, from which the identities discussed earlier are derivable as special cases. Master identities are also obtained which lead to cyclic identities with alternating signs. We discuss an extension of our results to pure imaginary and complex shifts as well as to the ratio of Jacobi theta functions.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Elliptic Equations
ID Code:83275
Deposited On:20 Feb 2012 06:29
Last Modified:20 Feb 2012 06:29

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