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.
Highlights
Solitons and integrable systems play an important role in nonlinear wave and dynamics systems
It has been significant in soliton theory to find more new integrable systems
The Casimir-Qiao-Liu equation (CQLE) (2) represents a third-order approximation of long wavelength, small amplitude waves of inviscid and incompressible fluids. It may be reduced from the two-dimensional Euler equation by an approximation procedure, and its solutions may be useful to construct new solvable potentials in Newtonian dynamics and to model electrophysiological phenomena in neuroscience
Summary
Solitons and integrable systems play an important role in nonlinear wave and dynamics systems. The CQLE (2) represents a third-order approximation of long wavelength, small amplitude waves of inviscid and incompressible fluids It may be reduced from the two-dimensional Euler equation by an approximation procedure, and its solutions may be useful to construct new solvable potentials in Newtonian dynamics and to model electrophysiological phenomena in neuroscience. Many integrable Hamiltonian systems of infinite dimensions with various physics and mathematical backgrounds have been obtained [16,17,18] When it comes to the integrable couplings, since they are based on semidirect sums of Lie algebras, the trace identity cannot be used properly. In this paper, starting from a new eigenvalue problem, the two-component Casimir-Qiao-Liu type hierarchy (2CQLTH) is worked out. By constructing the enlarged spectral problem, we obtain the the bi-integrable couplings of the 2-CQLTH.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
