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

Abstract

<abstract><p>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 $ (m, 3N-m) $-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.</p></abstract>