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 p...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.展开更多
This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition q = r.
A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The...A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The zero-curvature representation for the （γn, σk ）-CKPH is derived. The reduction and constrained flows of （γn, σk ）-CKPH are studied.展开更多
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)
文摘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NSFC (10671187 10971109)the Program for NCET (NECT-08-0515)
文摘This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition q = r.
基金Supported by National Basic Research Program of China(973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant Nos.10901090,10801083,11171175+1 种基金Chinese Universities Scientific Fund under Grant No.2011JS041China Postdoctoral Science Foundation Funded Project under Grant No.20110490408
文摘A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The zero-curvature representation for the （γn, σk ）-CKPH is derived. The reduction and constrained flows of （γn, σk ）-CKPH are studied.
