Abstract
A new (2+1)-dimensional lattice equation is presented based uponthe first two members in the hierarchy of thecombined Toda lattice and relativistic Toda lattice (TL-RTL)equations in (1+1) dimensions. A Darboux transformation for the hierarchyof the combined TL-RTL equations is constructed.Solutions of the first two members in the hierarchy of thecombined TL-RTL equations, as well as the new (2+1)-dimensional latticeequation are explicitly obtained by the Darboux transformation.
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