Application of Hirota's bilinear formalism to a two-dimensional lattice by Leznov

Abstract We consider the Leznov lattice in this paper. By a dependent variable transformation, the Leznov lattice is transformed into a quadri-linear form. This form is further transformed into a bilinear form by the introduction of an auxiliary variable. We present a Backlund transformation and a nonlinear superposition formula for the Leznov lattice. As an application of the results, soliton solutions and lump solutions are derived. Besides, starting from the bilinear BT, a Lax pair for the Leznov lattice is obtained.

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