(3+1)维时空分数阶偏微分方程mKdV-ZK方程的新精确解

New exact solutions for the (3+1)-dimensional space-time fractional mKdV-ZK equation

作者：洪韵(四川师范大学数学与软件科学学院)；孙峪怀(四川师范大学数学与软件科学学院)；江林(四川师范大学数学与软件科学学院)；张雪(四川师范大学数学与软件科学学院)

Author：HONG Yun(College of Mathematics and Software Science, Sichuan Normal University)；SUN Yu-Huai(College of Mathematics and Software Science, Sichuan Normal University)；JIANG Lin(College of Mathematics and Software Science, Sichuan Normal University)；ZHANG Xue(College of Mathematics and Software Science, Sichuan Normal University)

收稿日期：2016-10-06 年卷（期）页码：2017,54(4):679-682

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：扩展的(G'/G)-展开法；(3+1)维时空分数阶mKdV-ZK方程；精确解

Key words：Extended (G'/G)-expansion method；The (3+1)-dimensional space-time fractional mKdV-ZK equation；Exact solution

基金项目：国家自然科学基金，四川省教育厅自然科学重点基金

中文摘要

(3+1)维时空分数阶偏微分方程mKdV-ZK方程精确解的构建重要而令人感兴趣.本文通过含三维空间、一维时间的分数阶复变换将分数阶mKdV-ZK 方程转化为非线性常微分方程,再引入新的辅助微分方程的解及其新的展开形式,构建了mKdV-ZK方程系列精确解.

英文摘要

It is very important and interesting to construct the exact solutions of the (3+1)-dimensional space-time fractional mKdV-ZK equation.Firstly, by using fractional complex transformation, mKdV-ZK equation was transformed into a nonlinear ordinary deferential equation, and then introducing extends (G'/G)-expansion method to construct the exact solution. A series of new exact solution for mKdV-ZK equations have been obtained.

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论文摘要

(3+1)维时空分数阶偏微分方程mKdV-ZK方程的新精确解

New exact solutions for the (3+1)-dimensional space-time fractional mKdV-ZK equation