On the hierarchy of partially invariant submodels of differential equations

Preprint English OPEN
Golovin, Sergey V.;

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 equ... View more
  • References (18)
    18 references, page 1 of 2

    [13] Chupakhin A P 1997 On barochronous gas motions Dokl. of Russ. Ac. of Sci. 352(5)

    [14] Chupakhin A P 1998 Barochronous gas motions. General properties and submodel of types (1,2) and (1,1) (Preprint: Lavrentyev Institute of Hydrodynamics, Novosibirsk. No. 4) (in Russian).

    [15] Ovsiannikov L V 2003 Symmetry of barochronous gas motions Sib. Math. J. 44(5) 857-866

    [16] Pukhnachev V V 2000 An integrable model of nonstationary rotationally symmetrical motion of ideal incompressible fluid Nonlinear Dynamics 22 101-109

    [17] Thailert K 2006 One class of regular partially invariant solutions of the Navier-Stokes equations Nonlinear Dynamics 43(4) 343-364

    [18] Pommaret J F 1978 Systems of partial differential equations and Lie pseudogroups. (Gordon and Vreach Science Publishers, Inc.: New York)

    [19] Ovsyannikov L V 1998 Hierarchy of invariant submodels of differential equations Dokl. Math. 58(1) 127-129

    [20] Olver P J 1986 Applications of Lie groups to differential equations. (New York: Springer-Verlag)

    [21] Pavlenko A S 2005 Symmetries and solutions of equations of two-dimensional motions of politropic gas Siberian Electronic Mathematical Reports (http://semr.math.nsc.ru) 2 291-307

    [22] Kulikovskij A G and Lyubimov G A 1965 Magnetohydrodynamics, (Addison-Wesley: Reading)

  • Similar Research Results (3)
  • Metrics
Share - Bookmark