Recursion operators for KP, mKP and Harry-Dym Hierarchies

Details Recursion operators for KP, mKP and Harry-Dym Hierarchies Recursion operators for KP, mKP and Harry-Dym Hierarchies

2010-10-05

arxiv.org/abs/1010.0780v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, accepted by Journal of Nonlinear Mathematical Physics(2010)

Scientific paper

In this paper, we give a unified construction of the recursion operators from the Lax representation for three integrable hierarchies: Kadomtsev-Petviashvili (KP), modified Kadomtsev-Petviashvili (mKP) and Harry-Dym under $n$-reduction. This shows a new inherent relationship between them. To illustrate our construction, the recursion operator are calculated explicitly for $2$-reduction and $3$-reduction.

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