In [18] 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 transformation between Jacobi's modular differential equation and the well-known Schwarzian differential equation is derived.
L. ROSATI, NUCCI, M.C. (2005). A Lie symmetry connection between Jacobi's modular differential equation and Schwarzian differential equation. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 12(2), 144-161 [10.2991/jnmp.2005.12.2.1].
A Lie symmetry connection between Jacobi's modular differential equation and Schwarzian differential equation
NUCCI, Maria Clara
2005
Abstract
In [18] 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 transformation between Jacobi's modular differential equation and the well-known Schwarzian differential equation is derived.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
