Constrained lattice-field hierarchies and Toda system with Block symmetry

Abstract

In this paper, we construct the additional $W$-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new integrable difference equations. Under a further reduction, the constrained two-lattice integrable systems can be combined into one single integrable system, namely the well-known one dimensional original Toda hierarchy. We prove that the one dimensional original Toda hierarchy has a nice Block Lie symmetry.

16 Pages, accepted for publication in International Journal of Geometric Methods in Modern Physics

References in corpus (4)

• The Extended Bigraded Toda hierarchy
• Solutions of bigraded Toda hierarchy
• Supersymmetric BKP systems and their symmetries
• Quantum Torus symmetry of the KP, KdV and BKP hierarchies

Cited by in corpus (3)

• On a new integrable generalization of the Toda lattice and a discrete Yajima-Oikawa system
• Integrability of a discrete Yajima-Oikawa system
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy