https://doi.org/10.1140/epjp/s13360-025-06572-x
Regular Article
The Darboux transformation for the Tu equation: the kink and dromion solutions
1
Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang Province, People’s Republic of China
2
Department of Mathematics, Huizhou University, Huizhou, Guangdong Province, People’s Republic of China
3
College of Mathematic and Information Science, Shandong Technology and Business University, Yantai, Shandong Province, People’s Republic of China
4
Yantai Key Laboratory of Big Data Modeling and Intelligent Computing, Yantai, Shandong Province, People’s Republic of China
Received:
8
February
2025
Accepted:
23
June
2025
Published online:
12
July
2025
We provide a detailed derivation of the Darboux transformation for the Tu equation. A compact determinant representation for the n-fold Darboux transformation of the system is constructed, and the nth-order solution is derived using this transformation. The exact solutions, including the kink solution and the dromion solution, are obtained through corresponding formulae. We discuss the evolution of both the kink and dromion solutions, and several new patterns are identified for the nonlinear integrable equations.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
