The purpose of this paper is to find the exact solutions of a (3 + 1)-dimensional non-integrable Korteweg-de Vries type (KdV-type) equation, which can be used to describe the stability of soliton in a nonlinear media with weak dispersion.
The authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional non-integrable KdV-type equation. The used approach formally derives the essential conditions for these solutions to exist.
The results show that the equation exists rogue waves, homoclinic breather waves and soliton waves. To better understand the dynamic behavior of these solutions, the authors analyze the propagation and interaction properties of the these solutions.
These results may help to investigate the local structure and the interaction of waves in KdV-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.
The authors express their sincere thanks to the Editor and Reviewers for their valuable comments. This work was supported by the Postgraduate Research and Practice Program of Education and Teaching Reform of CUMT under Grant No. YJSJG_2018_036, the Qinglan Engineering project of Jiangsu Universities, the National Natural Science Foundation of China under Grant No. 11301527 and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.
Mao, J., Tian, S. and Zhang, T. (2019), "Rogue waves, homoclinic breather waves and soliton waves for a (3 + 1)-dimensional non-integrable KdV-type equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 2, pp. 763-772. https://doi.org/10.1108/HFF-06-2018-0287Download as .RIS
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