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On Invariants of Second Order Linear Partial Differential Equations in Two Variables

In: Algebra and Operator Theory

Author

Listed:
  • U. Bekbaev

    (Uzbekistan Academy of Sciences, Institute of Mathematics)

Abstract

In this paper we deal with second order linear partial differential equations (d.e.) over an abstract differential field (F,∂ 1, ∂ 2) of characteristic zero, define an analogue of transformations of ”indeterminates” (special transformations of ∂ 1 and ∂ 2) for such a differential field, consider equivalence of such d.e. relative to these transformations of ∂ 1, ∂ 2 and multiplications the unknown element of the d.e. by any element of F*. This equivalence will be reduced to a more simple one (Theorem 1), the corresponding field of invariant differential rational functions will be described (Theorem 2) and separation of“common type orbits” by invariants will be shown (Theorem 3). An analogical result was presented in [3].

Suggested Citation

  • U. Bekbaev, 1998. "On Invariants of Second Order Linear Partial Differential Equations in Two Variables," Springer Books, in: Yusupdjan Khakimdjanov & Michel Goze & Shavkat A. Ayupov (ed.), Algebra and Operator Theory, pages 145-156, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5072-9_12
    DOI: 10.1007/978-94-011-5072-9_12
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