Discrete generalized Darboux transformation and rational solutions for the three-field Blaszak-Marciniak lattice equation

Abstract

Under consideration is the discrete three-field Blaszak-Marciniak lattice equation. Firstly, this discrete equation is mapped to the continuous nonlinear equations under the continuous limit. Secondly, the generalized -fold Darboux transformation of this discrete equation is constructed and established. Finally, by applying the resulting Darboux transformation, some singular rational solutions and mixed exponential-rational solutions are presented, in particular, their limit state analysis and singular trajectories are analyzed graphically. These results may be helpful to explain some relevant physical phenomena.

Keywords

• three-field blaszak-marciniak equation
• continuous limit
• discrete generalized $ (m， 3n-m) $-fold darboux transformation
• rational solutions
• limit state analysis