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

Ting Zhang; Xiaoyong Wen; Ting Zhang; Xiaoyong Wen

doi:10.3934/math.2023793

AIMS Mathematics

2023, Volume 8, Issue 7: 15553-15568. doi: 10.3934/math.2023793

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Research article

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

Ting Zhang ,
Xiaoyong Wen ^,

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received: 24 February 2023 Revised: 02 April 2023 Accepted: 03 April 2023 Published: 27 April 2023
MSC : 35Q51, 35Q35, 37K40

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.
Citation: Ting Zhang, Xiaoyong Wen. Discrete generalized Darboux transformation and rational solutions for the three-field Blaszak-Marciniak lattice equation[J]. AIMS Mathematics, 2023, 8(7): 15553-15568. doi: 10.3934/math.2023793

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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, 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.

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