Wronskian, Pfaffian and periodic wave solutions for a $$(2 + 1)$$(2+1)-dimensional extended shallow water wave equation
Wronskian, Pfaffian and periodic wave solutions for a $$(2 + 1)$$(2+1)-dimensional extended shallow water wave equation
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DOI：
10.1007/s11071-017-3630-y
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发表时间：
2017-07
影响因子：
5.6
通讯作者：
Qian-Min Huang;Yi-Tian Gao
中科院分区：
文献类型：
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作者：
Qian-Min Huang;Yi-Tian Gao
本文研究的是一维扩展浅水波方程。通过广义因变量变换得到双线性形式。分别用Wronskian方法和Pfronskian方法得到了N阶解析解。通过N阶解构造孤子解。对孤子传输的讨论表明，有变换的孤子解比无变换的孤子解更一般，并且会影响孤子解的性质，这是一个与上述变换有关的真实的函数。通过Hirota-Riemann方法得到了单周期波解。研究了单周期波解与单孤子解之间的关系，指出在一定条件下单周期波解可以逼近单孤子解。
Under investigation in this paper is a-dimensional extended shallow water wave equation. Bilinear form is obtained via the generalized dependent variable transformation. TheNth-order analytic solutions are, respectively, obtained via the Wronskian and Pfaffian techniques. Soliton solutions are constructed through theNth-order solutions. Discussions on the propagation of the solitons indicate that the soliton solutions withare more general than those without, andcould affect the features of the soliton solutions, whereis a real function related to the aforementioned transformation. One-periodic wave solutions are obtained via the Hirota–Riemann method. Relation between the one-periodic wave solutions and one-soliton solutions is studied, which indicates that the one-periodic wave solutions can approach to the one-soliton solutions under certain condition.