文献类型：期刊文献

英文题名：The Darboux transformation for the Tu equation: the kink and dromion solutions

作者：Zhang, Yongshuai[1];Qiu, Deqin[2];Liu, Wei[3,4]

机构：[1]Shaoxing Univ, Dept Math, Shaoxing, Zhejiang, Peoples R China;[2]Huizhou Univ, Dept Math, Huizhou, Guangdong, Peoples R China;[3]Shandong Technol & Business Univ, Coll Math & Informat Sci, Yantai, Shandong, Peoples R China;[4]Yantai Key Lab Big Data Modeling & Intelligent Com, Yantai, Shandong, Peoples R China

年份：2025

卷号：140

期号：7

外文期刊名：EUROPEAN PHYSICAL JOURNAL PLUS

收录：SCI-EXPANDED(收录号：WOS:001526731600001)、、Scopus(收录号：2-s2.0-105010637721)、WOS

基金：This work is supported by the National Natural Science Foundation of China (Grant Nos. 12301308 and 12171433), the Doctoral Research Foundation Project of Huizhou University (Grant No. 2022JB039), and the Project of Guangdong Provincial Department of Education (Grant No. 2021ZDJS080), Teaching Quality and Teaching Reform Engineering Construction Project of Huizhou University (Grant No. 2023158), and Fundamental Research Projects of Science and Technology Innovation and Development Plan in Yantai City (Grant No. 2023YT06000660).

语种：英文

外文摘要：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.