×

Cyclic identities for Jacobi elliptic and related functions. (English) Zbl 1062.33020

Summary: 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.

MSC:

33E05 Elliptic functions and integrals
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Khare A., J. Math. Phys. 43 pp 3798– (2002) · Zbl 1060.33026 · doi:10.1063/1.1484541
[2] Khare A., Phys. Rev. Lett. 88 pp 244101– (2002) · doi:10.1103/PhysRevLett.88.244101
[3] Cooper F., J. Phys. A 35 pp 10085– (2002) · Zbl 1039.35098 · doi:10.1088/0305-4470/35/47/309
[4] A. Khare, A. Lakshminarayan, and U. Sukhatme, ”Cyclic Identities Involving Jacobi Elliptic Functions, II,” math-ph/0207019 (2002). · Zbl 1060.33026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.