Symmetry classification of KdV-type nonlinear evolution equations


Gungor F., Lahno V., Zhdanov R.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.45, ss.2280-2313, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 45 Konu: 6
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1063/1.1737811
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS
  • Sayfa Sayıları: ss.2280-2313

Özet

Group classification of a class of third-order nonlinear evolution equations generalizing KdV and mKdV equations is performed. It is shown that there are two equations admitting simple Lie algebras of dimension three. Next, we prove that there exist only four equations invariant with respect to Lie algebras having nontrivial Levi factors of dimension four and six. Our analysis shows that there are no equations invariant under algebras which are semi-direct sums of Levi factor and radical. Making use of these results we prove that there are three, nine, thirty-eight, fifty-two inequivalent KdV-type nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively. Finally, we perform a complete group classification of the most general linear third-order evolution equation. (C) 2004 American Institute of Physics.