Chin. Phys. B, 2021, Vol. 30(1): 010202    DOI: 10.1088/1674-1056/abb3f3
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# High-order rational solutions and resonance solutions for a (3+1)-dimensional Kudryashov-Sinelshchikov equation

Yun-Fei Yue(岳云飞)1, Jin Lin(林机)2, and Yong Chen(陈勇)1,2,3,
1 School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China; 2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China; 3 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Abstract  We mainly investigate the rational solutions and N-wave resonance solutions for the (3+1)-dimensional Kudryashov-Sinelshchikov equation, which could be used to describe the liquid containing gas bubbles. With appropriate transformations, two kinds of bilinear forms are derived. Employing the two bilinear equations, dynamical behaviors of nine district solutions for this equation are discussed in detail, including bright rogue wave-type solution, dark rogue wave-type solution, bright W-shaped solution, dark W-shaped rational solution, generalized rational solution and bright-fusion, dark-fusion, bright-fission, and dark-fission resonance solutions. In addition, the generalized rational solutions, which depending on two arbitrary parameters, have an interesting structure: splitting from two peaks into three peaks.
Keywords:  rational solution      N-wave resonance solution      Hirota bilinear method      Kudryashov-Sinelshchikov equation
Received:  10 August 2020      Revised:  01 January 1900      Accepted manuscript online:  01 September 2020
 PACS: 02.30.Ik (Integrable systems) 05.45.Yv (Solitons) 04.20.Jb (Exact solutions)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11675054), the Future Scientist/Outstanding Scholar Training Program of East China Normal University (Grant No. WLKXJ2019-004), the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213), and the Project from the Science and Technology Commission of Shanghai Municipality, China (Grant No. 18dz2271000).
Corresponding Authors:  Corresponding author. E-mail: ychen@sei.ecnu.edu.cn