Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies

Abstract

We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a B type reduction condition of this integrable hierarchy. Further we show that the D type Drinfeld-Sokolov hierarchy, which is a reduction of the two-component BKP hierarchy, possess a complete Block type additional symmetry algebra. That D type Drinfeld-Sokolov hierarchy has a similar algebraic structure as the bigraded Toda hierarchy which is a differential-discrete integrable system.

16 pages, accepted for publication in the Journal of Mathematical Physics

References in corpus (6)

• The Extended Bigraded Toda hierarchy
• Block type symmetry of bigraded Toda Hierarchy
• Dispersionless bigraded Toda Hierarchy and its additional symmetry
• Solutions of bigraded Toda hierarchy
• From Additional Symmetries to Linearization of Virasoro Symmetries
• Infinite-dimensional 3-algebra and integrable system

Cited by in corpus (10)

• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• Supersymmetric BKP systems and their symmetries
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions
• Block (or Hamiltonian) Lie symmetry of dispersionless D type Drinfeld-Sokolov hierarchy
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• Quantum Torus symmetries of the CKP and multi-component CKP hierarchies
• Virasoro symmetry of the constrained multi-component KP hierarchy and its integrable discretization
• Constrained lattice-field hierarchies and Toda system with Block symmetry
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy
• Addition formulae of discrete KP, q-KP and two-component BKP systems