On the Superextension of the Kadomtsev-Petviashvili Equation and Finite-Gap Solutions of Korteweg-de Vries Superequations

  • P. I. Holod
  • S. Z. Pakuliak
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

It was shown in Ref. [1, 2], that there exist two ways for the nonlinear integrable Korteweg — de Vries equation to be super-generalized. One of this equations [1] proves to be, in fact, super-symmetric (involutory integrals of motion for this equation commute with the generator of global supertransformation), and another one [4] is bi-Hamiltonian system, i.e. the integrals of motion, which are in involution, satisfy the relations [3]
$$ {\Omega _1}(\delta {H_{n + 1}}) = {\Omega _2}(\delta {H_n}) $$
(1)
where Ω1 and Ω2 are the first and the second Hamiltonian structures for s-KdV superequation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • P. I. Holod
    • 1
  • S. Z. Pakuliak
    • 1
  1. 1.Institute for Theoretical PhysicsKiev 130USSR

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