This article is cited in 7 papers

Multicomponent fractional Volterra hierarchy and its subhierarchy with Virasoro symmetry

Chuanzhong Li

School of Mathematics and Statistics, Ningbo University, Ningbo, Zhejiang, China

Abstract: Using the Hamiltonian structures and tau symmetries, we construct a multicomponent fractional Volterra hierarchy (MFVH) as an example of a generalized integrable system. We study the Hirota bilinear equation and the Virasoro symmetry for this hierarchy. As a reduction of the MFVH from a commutative subalgebra, we construct the fractional $Z_N$-Volterra hierarchy and its Virasoro symmetry.

Keywords: multicomponent fractional Volterra hierarchy, fractional $Z_N$-Volterra hierarchy, additional symmetry, Virasoro Lie algebra.

MSC: 37K05, 37K10, 35Q53

Received: 20.11.2020
Revised: 26.12.2020

DOI: 10.4213/tmf10010

 English version: Theoretical and Mathematical Physics, 2021, 207:1, 397–414

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