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

الملخص EN

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 of 3×3 block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.