Abstract
We extend the two-dimensional Toda lattice hierarchy (2DTLH) by its squared eigenfunction symmetries. This extended 2DTLH (ex2DTLH) includes the two-dimensional Toda lattice equation with self-consistent sources (2DTLSCS) as its first nontrivial equation. Lax representation of ex2DTLH is also presented. With the help of the Lax representation, we construct a nonauto-Bäcklund Darboux transformation (DT) for 2DTLSCS by applying the variation of constants to 2DTLSCS auto-Bäcklund DT. This DT enables us to find many solutions to 2DTLSCS, including solitons, rational solutions, positons, negatons, and complexitons.
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