Dispersionless bigraded Toda Hierarchy and its additional symmetry

Abstract

In this paper, we firstly give the definition of dipersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov-Schulman's $\M_L$, $\M_R$ operator and give the additional Block symmetry of dBTH. Meanwhile we give tau function of dBTH and some some related dipersionless bilinear equations.

31 pages, Accepted by Reviews in Mathematical Physics

References in corpus (3)

• The Extended Bigraded Toda hierarchy
• Block type symmetry of bigraded Toda Hierarchy
• Solutions of bigraded Toda hierarchy

Cited by in corpus (15)

• The extended $Z_N$-Toda hierarchy
• Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies
• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• On the extended multi-component Toda hierarchy
• Quantum Torus symmetry of the KP, KdV and BKP hierarchies
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions
• Block (or Hamiltonian) Lie symmetry of dispersionless D type Drinfeld-Sokolov hierarchy
• Sato theory on the $q$-Toda hierarchy and its extension
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• Quantum Torus symmetries of the CKP and multi-component CKP hierarchies
• Quantum torus algebras and B(C) type Toda systems
• Multi-fold Darboux transformations of the extended bigraded Toda hierarchy
• Constrained lattice-field hierarchies and Toda system with Block symmetry
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy
• A strongly coupled extended Toda hierarchy and its Virasoro symmetry