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arXiv · 2510.14426

Bilinear structures of the fourth-order lattice Gel'fand-Dikii equations

Song-lin Zhao·Han Wang·Da-jun Zhang
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Abstract

In this paper we derive bilinear forms and present their solutions in Casoratians for several fourth-order lattice Gel'fand-Dikii (lattice GD-4) equations. These equations were recently formulated from the direct linearization approach and exhibit the multidimensionally consistent property in multi-component form. Based on the obtained soliton solutions, we are able 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 Casoratian solutions are provided.

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Song-lin Zhao, Han Wang, Da-jun Zhang. 2025-10-16. Bilinear structures of the fourth-order lattice Gel'fand-Dikii equations. https://arxiv.org/abs/2510.14426

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