Conservation laws, periodic and rational solutions for an extended modified Korteweg-de Vries equation
Conservation laws, periodic and rational solutions for an extended modified Korteweg-de Vries equation
复制标题
扩展修正 Korteweg-de Vries 方程的守恒定律、周期解和有理解
DOI：
10.1007/s11071-018-4143-z
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发表时间：
2018
影响因子：
5.6
通讯作者：
Wang Lei
中科院分区：
文献类型：
--
作者：
Wang Xin;Zhang Jianlin;Wang Lei
研究了一个可积的扩展的修正的Korteweg-de弗里斯方程，它包含了五阶色散和相应的高阶非线性项.基于Lax对构造了无穷多个守恒律。利用N重Darboux变换（DT）得到了广义N阶周期解，并利用极限方法从广义DT得到了N阶有理解的一个简单表示.作为应用，给出了一阶到二阶的周期解和有理解，并给出了一些典型的非线性波型，如双周期格状波和双局域高峰值波.有趣的是，由于高阶项的存在，双局域高峰值波在二阶有理解中可以转化为W形孤立子。
We study an integrable extended modified Korteweg–de Vries equation, which contains the fifth-order dispersion and relevant higher-order nonlinear terms. The infinitely many conservation laws are constructed based on the Lax pair. A generalNth-order periodic solution is obtained by means of theN-fold Darboux transformation (DT), and a simple representation of theNth-order rational solution is derived from the generalized DT by using the limit approach. As an application, the explicit periodic and rational solutions from first to second order are given, and some typical nonlinear wave patterns such as the doubly periodic lattice-like and doubly localized high-peak waves are shown. It is interestingly found that, the doubly localized high-peak wave can be converted into a W-shaped soliton in the second-order rational solution due to the existence of higher-order terms.