A novel kind of a multicomponent hierarchy of discrete soliton equations and its application

Zhenbo Wang^a, Haifeng Wang^b, and Yufeng Zhang^a^,*

^aSchool of Mathematics, China University of Mining and Technology, Xuzhou, China

^bSchool of Science, Jimei University Xiamen, Fujian, China

email: *zhangyfcumt@163.com

Received 19 September, 2022

Abstract— Based on a Lie algebra \(\hat g\), we presented a method for constructing multicomponent integrable hierarchies of discrete soliton equations. As an application of the method, we consider the modified Toda spectral problem and obtain a new multicomponent integrable hierarchy of lattice equations with two arbitrary constants, which can be reduced to two multicomponent integrable systems, one of which is the famous Toda lattice system.

Keywords: multicomponent hierarchy of discrete soliton equations, Lie algebra \(\hat g\), generalized Toda spectral problem

DOI: 10.1134/S0040577923060065