On the hierarchy of partially invariant submodels of differential equations

Details On the hierarchy of partially invariant submodels of differential equations On the hierarchy of partially invariant submodels of differential equations

2007-11-15

arxiv.org/abs/0711.2338v1

J. Phys. A: Math. Theor. 2008 41 265501

Physics

Mathematical Physics

Scientific paper

10.1088/1751-8113/41/26/265501

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given.

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