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A hierarchy of lattice soliton equations and its Darboux transformation
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2004
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Spectral TheoryEngineeringPhysicsTrace IdentityTopological SolitonQuantum Field TheoryLattice Soliton EquationsBacklund TransformationIntegrable SystemLattice Soliton EquationLattice TheoryDiscrete Integrable System
A new discrete spectral problem is introduced and the corresponding hierarchy of the lattice soliton equations are derived by means of the trace identity. We find a new Darboux transformation of the lattice soliton equation, through which the explicit solutions are shown.