Abstract
A Darboux transformation is presented for the Volterra lattice equation, based on a pair of $$2\times 2$$ matrix spectral problems. The resulting DT is applied to construction of solitary wave solutions from a constant seed solution. A particular phenomenon is that only one condition is required in determining the corresponding Darboux matrix, but not two as for most pairs of $$2\times 2 $$ matrix spectral problems.
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