摘要
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 {Φ i , Ψ i } are presented explicitly. Furthermore, we show that acting on the space of the wave operator, *k forms new centerless W cC 1+∞ and W cB 1+∞ -subalgebra of centerless W 1+∞ respectively. In order to define above symmetry flows *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.
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 {Φ i , Ψ i } are presented explicitly. Furthermore, we show that acting on the space of the wave operator, ＊k forms new centerless W cC 1＋∞ and W cB 1＋∞ -subalgebra of centerless W 1＋∞ respectively. In order to define above symmetry flows ＊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.
基金
supported by National Natural Science Foundation of China (Grant Nos. 10971109, 10971209)
the Program for New Century Excellent Talents in University (Grant No. NCET-08-0515)
