Finding Lie Symmetries of Partial Differential Equations with MATHEMATICA$^{®}$: Applications to Nonlinear Fiber Optics

Pulov, Vladimir; Uzunov, Ivan; Chacarov, Edy

doi:10.7546/giq-9-2008-280-291

VOL. 9 | 2008 Finding Lie Symmetries of Partial Differential Equations with MATHEMATICA$^{®}$: Applications to Nonlinear Fiber Optics

Chapter Author(s) Vladimir Pulov, Ivan Uzunov, Edy Chacarov

Editor(s) Ivaïlo M. Mladenov

Geom. Integrability & Quantization, 2008: 280-291 (2008) DOI: 10.7546/giq-9-2008-280-291

Abstract

A MATHEMATICA$^{®}$ package for finding Lie symmetries of partial differential equations is presented. The package has been applied to perform a full Lie group analysis of basic models of nonlinear fiber optics. As a result of this group invariant solutions have been obtained. Comparisons with earlier published computer algebra implementations of the Lie group method are discussed.