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Finding Lie symmetries of partial differential equations with {MATHEMATICA}\(^\circledR\): 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\(^\circledR\) 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.
For the entire collection see [Zbl 1154.17001].

MSC:

65Y15 Packaged methods for numerical algorithms
35A30 Geometric theory, characteristics, transformations in context of PDEs
35B06 Symmetries, invariants, etc. in context of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
68W30 Symbolic computation and algebraic computation

Software:

LieSymm; Mathematica
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