Integrability on generalized q-Toda equation and hierarchy

Abstract

In this paper, we construct a new integrable equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized q-Toda equation and a whole integrable generalized q-Toda hierarchy are also constructed. To show the integrability, the Bi-Hamiltonian structure and tau symmetry of the generalized q-Toda hierarchy are given and this leads to the tau function.

Keywords:

• generalized q-Toda lattice
• soliton solutions
• Lax equation
• generalized q-Toda hierarchy
• tau function

2000 Mathematics Subject Classification:

• 37K05
• 37K10
• 37K20