Complexiton and resonant multiple wave solutions to the (2+1)-dimensional Konopelchenko-Dubrovsky equation
Complexiton and resonant multiple wave solutions to the (2+1)-dimensional Konopelchenko-Dubrovsky equation
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DOI：
10.1016/j.camwa.2018.05.024
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Pinxia Wu;Yufeng Zhang;Iqbal Muhammad;Qiqi Yin
中科院分区：
文献类型：
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作者：
Pinxia Wu;Yufeng Zhang;Iqbal Muhammad;Qiqi Yin
摘要本文研究了（2+ 1）维Konopelchenko-Dubrovsky （KD）方程。利用Hirota直接法和线性叠加原理，成功地构造了配合子和共振多波解。对于Hirota直接法，关键是找到KD方程的双线性形式，并在实场中应用其2n -孤子公式来建立共轭波变量对作用下的n -络合子解。指数行波在实场中的线性叠加可以产生共振型多波解，然后将线性叠加原理推广到复场，得到一些新的共振型多波解。用图形给出了配色、共振多重波和新型共振多重波型解的现象。
Abstract In this paper, the (2+ 1)-dimensional Konopelchenko–Dubrovsky (KD) equation is investigated. Using the Hirota direct method and linear superposition principle, the complexiton and resonant multiple wave solutions are successfully constructed. For the Hirota direct method, it is essential that finding the bilinear form to the KD equation and applying its 2 N-soliton formulation in real field to build the N-complexiton solutions under the action of pairs of conjugate wave variables. The linear superposition in real field of exponential traveling waves can generate the resonant multiple wave solutions, and then generalize linear superposition principle to complex field, we obtain some new resonant multiple wave type solutions. The phenomena of complexiton, resonant multiple wave and new resonant multiple wave type solutions are presented by figures.