2002/04/30 by Avinash Khare, Khare, Avinash, Uday Sukhatme +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.math-ph/0204054
11 pages
arxiv created 2002/04/30 · openalex publication_date 2002/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. We obtain and discuss significant generalizations of the celebrated Landen formulas. Our approach is based on some recently obtained periodic solutions of physically interesting nonlinear differential equations and numerous remarkable new cyclic identities involving Jacobi elliptic functions.