https://doi.org/10.1140/epjs/s11734-025-01862-y
Regular Article
Local and nonlocal self-dual network equations: bilinear approach and asymptotic analysis
1
School of Mathematics and Statistics, Changshu Institute of Technology, 215500, Suzhou, China
2
School of Mathematical Sciences, Zhejiang University of Technology, 310023, Hangzhou, China
3
Department of Mathematics, Shanghai University, 200444, Shanghai, China
4
Newtouch Center for Mathematics of Shanghai University, 200444, Shanghai, China
Received:
27
March
2025
Accepted:
8
August
2025
Published online:
19
August
2025
This paper investigates the nonlinear self-dual network models, including both classical and nonlocal cases. Double Casoratian solutions to the unreduced four-potential Ablowitz–Ladik system and its corresponding bilinear forms are presented. In addition to some known reductions, we propose three novel reductions to the unreduced system, namely, the complex reverse-space, the reverse-space-time, and the complex reverse-space-time self-dual network models. These equations are well suited for Casoratian solution reductions. Furthermore, a classification of solutions with respect to the distribution of the eigenvalues and for general parameters is provided. As for illustrations, solutions to the classical nonlinear self-dual network equation, the reverse-time nonlocal self-dual network equation and the reverse-space-time nonlinear self-dual network equation are discussed.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
