Bilinearization and solutions of the fourth-order lattice Gel'fand-Dikii type equations

Abstract

In this paper we derive bilinear forms and solutions in Casoratians for some fourth-order lattice Gel'fand-Dikii (lattice GD-4) type equations. These equations were recently formulated from the direct linearization approach and exhibit multidimensionally consistent property in multi-component form. The obtained solitons and Casoratian forms enable us to extend these equations by introducing a parameter $\delta$. These $\delta$-extended lattice GD-4 type equations are still consistent around the cube, and their bilinear forms together with Casoration solutions are presented.

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