Localized waves and interaction solutions to an integrable variable coefficient Date-Jimbo-Kashiwara-Miwa equation

Abstract

This paper initiates an exploration into the exact solutions of the variable coefficient Date-Jimbo-Kashiwara-Miwa equation, first utilizing the Painlevé analysis method to discuss the integrability of the equation. Subsequently, By employing the Hirota bilinear method, N-soliton solutions for the equation are constructed. The application of the Long wave limit method to these N-soliton solutions yields rational and semirational solutions. Various types of localized waves, encompassing solitons, lumps, breather waves, and others, emerge through the careful selection of specific parameters. By analyzing the image of the solutions, the evolution process and its dynamical behavior are studied.

Keywords:

• Hirota bilinear method
• long wave limit
• Painlevé analysis
• interaction solutions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11505090), Liaocheng University level science and technology research fund No. 318012018, Discipline with Strong Characteristics of Liaocheng University –Intelligent Science and Technology under Grant No. 319462208, Research Award Foundation for Outstanding Young Scientists of Shandong Province (No. BS2015SF009) and the doctoral foundation of Liaocheng University under Grant No. 318051413.

Notes on contributors

Jinzhou Liu

Jinzhou Liu, a graduate student at Liaocheng University in China, specializes in research on soliton integrable systems and exact solutions for partial differential equations. During his academic tenure, he has been awarded the first-class scholarship multiple times and has published numerous SCI papers.

Xinying Yan

Xinying Yan, also a graduate student at Liaocheng University in China, primarily focuses on dissipative dynamic systems' structure-preserving algorithms and their application research in wave dynamics and aerospace dynamics issues. During her tenure at the university, she has published several SCI papers.

Meng Jin

Meng Jin, another graduate student at Liaocheng University in China, concentrates on the study of soliton integrable systems and the direction of exact solutions for partial differential equations. He has published multiple SCI papers.

Xiangpeng Xin

Xiangpeng Xin, an associate professor at Liaocheng University in China, has presided over two projects funded by the Natural Science Foundation, including one National Youth Foundation project, one Shandong Provincial Doctoral Fund, and has participated in multiple provincial funds. Additionally, he has been involved in one university-level educational reform project. His main research direction is soliton integrable systems.