Finding Lie symmetries of partial differential equations with MATHEMATICA
: Applications to nonlinear fiber optics. (English) Zbl 1192.65171
Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 280-291 (2008).
Summary: A Mathematica package for finding Lie symmetries of partial differential equations is presented. The package is applied to perform a full Lie group analysis of basic models of nonlinear fiber optics. As a result of this, group invariant solutions are obtained. Comparisons with earlier published computer algebra implementations of the Lie group method are discussed.
|65Y15||Packaged methods in numerical analysis|
|35A30||Geometric theory for PDE, characteristics, transformations|
|35B06||Symmetries, invariants, etc. (PDE)|
|35Q60||PDEs in connection with optics and electromagnetic theory|
|68W30||Symbolic computation and algebraic computation|