A Liouville integrable lattice soliton equation, infinitely many conservation laws and integrable coupling systems

A lattice soliton equation is proposed as a typical lattice system in the hierarchy of lattice soliton equations, which is derived from a discrete matrix spectral problem. The Liouville integrability for the corresponding lattice system is demonstrated. Moreover, infinitely many conservation laws of corresponding lattice system are obtained by a direct way. Finally, the integrable coupling systems of corresponding lattice systems are deduced through enlarging associated Lax pairs.