J C Ndogmo 2008 J. Phys. A: Math. Theor. 41 102001 doi:10.1088/1751-8113/41/10/102001
A method for the equivalence group and its infinitesimal generators
FREE ARTICLEJ C Ndogmo
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We give an effective method for the systematic determination of the equivalence group for any family of differential equations, and for the determination of the infinitesimal generators of this group. This is achieved by viewing the equivalence group as a projected subgroup related to the full symmetry group of the equation, in which the coefficients specifying the family element in the equation are also considered as dependent variables. The method is extended to provide the exact number of fundamental invariants of the equation, without any prior calculation of these invariants. It is then applied to review a number of results obtained in the recent literature on the subject of invariant functions of differential equations. The method is also applied, probably for the first time, to a case of nonlinear equation.
- PACS
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02.30.Jr Partial differential equations
- MSC
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22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
20B35 Subgroups of symmetric groups
22E40 Discrete subgroups of Lie groups (See also 20Hxx, 32Nxx)
- Subjects
- Dates
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Issue 10 (14 March 2008)
Received 22 December 2007, in final form 27 January 2008
Published 26 February 2008
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A method for the equivalence group and its infinitesimal generators
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