Additional symmetries of constrained CKP and BKP hierarchies

Details Additional symmetries of constrained CKP and BKP hierarchies Additional symmetries of constrained CKP and BKP hierarchies

2010-07-16

arxiv.org/abs/1007.2701v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, accepted by SCIENCE CHINA Mathematics(2010)

Scientific paper

The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented explicitly. Furthermore, we show that acting on the space of the wave operator, $\partial_k^*$ forms new centerless $W^{cC}_{1+\infty}$ and $W^{cB}_{1+\infty}$-subalgebra of centerless $W_{1+\infty}$ respectively. In order to define above symmetry flows $\partial_k^*$ of the cCKP and cBKP hierarchies, two vital operators $Y_k$ are introduced to revise the additional symmetry flows of the CKP and BKP hierarchies.

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