Characteristics of the solitary waves and lump waves with interaction phenomena in a (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation
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In this paper, we consider a (\(2+1\))-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada (gCDGKS) equation, which is a higher-order generalization of the celebrated Kadomtsev–Petviashvili (KP) equation. By considering the Hirota bilinear form of the CDGKS equation, we study a type of exact interaction waves by the way of vector notations. The interaction solutions, which possess extensive applications in the nonlinear system, are composed by lump wave parts and soliton wave parts, respectively. Under certain conditions, this kind of solutions can be transformed into the pure lump waves or the stripe solitons. Moreover, we provide the graphical analysis of such solutions in order to better understand their dynamical behavior.
KeywordsThe (\(2+1\))-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation Hirota bilinear form Interaction waves Lump waves Soliton waves
The authors would like to thank the editor and the referees for their valuable comments and suggestions. This work was supported by the Research and Practice of Educational Reform for Graduate students in China University of Mining and Technology under Grant No. YJSJG_2017_049, the No.  22 supported by Ministry of Industry and Information Technology of China, the Qinglan Engineering project of Jiangsu Universities, the National Natural Science Foundation of China under Grant Nos. 11301527 and 51522902, the Fundamental Research Funds for the Central Universities under Grant No. DUT17ZD233, and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.
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No potential conflict of interest was reported by the authors.
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