@article{Zhang2023, 
author = {Ting Zhang and Xiaoyong Wen},
title = {Discrete generalized Darboux transformation and rational solutions for the three-field Blaszak-Marciniak lattice equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {15553-15568},
keywords = {three-field Blaszak-Marciniak equation, continuous limit, discrete generalized (m, 3N−m)-fold Darboux transformation, rational solutions, limit state analysis},
url = {https://www.sciopen.com/article/10.3934/math.2023793},
doi = {10.3934/math.2023793},
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    (  m  ,  3  N  −  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.}
}