The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures

Abstract

A new type of two-component Casimir-Qiao-Liu type hierarchy (2-CQLTH) is produced from a new spectral problem and their bi-Hamiltonian structures are constructed. Particularly, a new completely integrable two-component Casimir-Qiao-Liu type equation (2-CQLTE) is presented. Furthermore, based on the semidirect sums of matrix Lie algebras consisting of3×3block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.