publication . Article . Other literature type . Preprint . 2007

On the hierarchy of partially invariant submodels of differential equations

S. V. Golovin;
Open Access
  • Published: 15 Nov 2007 Journal: Journal of Physics A: Mathematical and Theoretical, volume 41, page 265,501 (issn: 1751-8113, eissn: 1751-8121, Copyright policy)
  • Publisher: IOP Publishing
Abstract
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.
Subjects
free text keywords: Modelling and Simulation, Statistics and Probability, Mathematical Physics, General Physics and Astronomy, Statistical and Nonlinear Physics, 76M60, 58J70, 76W05, 35C05, Algebra, Differential equation, Invariant (mathematics), Mathematical analysis, System of differential equations, Regular solution, Magnetohydrodynamics, Hierarchy, Mathematics, Enumeration, Equivalence (measure theory)
Related Organizations
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