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.

13 pages, to appear in Journal of Nonlinear Mathematical Physics, Vol. 21 nr.3 (2014)

References in corpus (2)

• q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
• Solutions of bigraded Toda hierarchy