A Lie Symmetry Connection between Jacobi's Modular Differential Equation and Schwarzian Differential Equation
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In  Jacobi introduced a third-order nonlinear ordinary differential equation which links two different moduli of an elliptic integral. In the present paper Lie group analysis is applied to that equation named Jacobi's modular differential equation. A six-dimensional Lie symmetry algebra is obtained and its symmetry generators are found to be given in terms of elliptic integrals. As a consequence the transformtion between Jacobi's modular differential equation and the well-known Schwarzian differential equation is derived.
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Cite this article
TY - JOUR AU - L. Rosati AU - M.C. Nucci PY - 2005 DA - 2005/05/01 TI - A Lie Symmetry Connection between Jacobi's Modular Differential Equation and Schwarzian Differential Equation JO - Journal of Nonlinear Mathematical Physics SP - 144 EP - 161 VL - 12 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2005.12.2.1 DO - 10.2991/jnmp.2005.12.2.1 ID - Rosati2005 ER -