Darboux transformation of the special (2+1)-dimensional Toda lattice and its explicit solution

In this paper, we study the following special (2+1)-dimensional Toda lattice: This lattice system can be reduced to two integrable (1+1)-dimensional (2D) differential–difference systems, and further into three consistent linear spectral problems. A Darboux transformation (DT) of the lattice system is derived by means of a gauge transformation. Moreover, a new explicit solution of the lattice system is obtained by using the DT and the compatibility of two 2D differential–difference systems.

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