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

2025/10/16 by Zhao, Song-lin, Wang, Han, Zhang, Da-jun
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2510.14426

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 δ. These δ-extended lattice GD-4 type equations are still consistent around the cube, and their bilinear forms together with Casoration solutions are presented.

Citations

• On the formulation of the NQC variable
• On the Dbar method and direct linearization approach of the lattice KdV type equations
• On trilinear and quadrilinear equations associated with the lattice Gel'fand-Dikii hierarchy
• Connection between the symmetric discrete AKP system and bilinear ABS lattice equations
• Discrete Boussinesq-type equations
• Notes on solutions in Wronskian form to soliton equations: KdV-type
• The Boussinesq integrable system. Compatible lattice and continuum structures

Related

• Notes on solutions in Wronskian form to soliton equations: KdV-type
• Multisoliton solution and super-bilinear form of lattice supersymmetric KdV equation
• On trilinear and quadrilinear equations associated with the lattice Gel'fand-Dikii hierarchy
• The Method of Hirota Bilinearization
• Nonlinearization of the KdV-type and mKdV-type bilinear equations