Multi-component matrix loop algebras and their applications to integrable systems

Abstract

Firstly, a multi‐component matrix Loop algebra Ã2M and its expanding Loop algebra Ã4M+1 are constructed. Then using Ã2M, an isospectral problem is established; and by virtue of the Tu scheme, a multi‐component integrable system is obtained, which is Liouville integrable. Further, the Hamiltonian structure of the obtained system is worked out by the trace identity. Finally, again using the Tu scheme, the integrable coupling of the obtained system is generated based on Ã4M+1.