三个非线性发展方程新的精确解的构造
发布时间：2018-08-05 17:01
【摘要】：(G'/G)-展开法是一种构建非线性发展方程精确解的强有力的数学工具.在本文中,我们讨论了三个方程.首先,运用修改的(G'/G)-展开法获得了三阶非线性波动方程的精确解；其次,利用分数阶复变换,将分数阶非线性发展方程转化为非线性常微分方程,运用扩展的(G'/G)-展开法获得了非线性分数阶Klein-Gordon方程的精确解；最后,利用修改的(G'/G)-展开法构建分数阶改进的Zakharov-Kuznetsov方程的精确解.一些更为丰富的新解被获得,包括双曲函数解、三角函数解、有理函数解和负幂次解等.
[Abstract]:(G / G) -expansion method is a powerful mathematical tool for constructing exact solutions of nonlinear evolution equations. In this paper, we discuss three equations. Firstly, the exact solution of the third order nonlinear wave equation is obtained by using the modified (GG / G) -expansion method. Secondly, the fractional nonlinear evolution equation is transformed into the nonlinear ordinary differential equation by using the fractional complex transformation. The exact solution of the nonlinear fractional Klein-Gordon equation is obtained by using the extended (G / G) -expansion method, and finally, the exact solution of the fractional modified Zakharov-Kuznetsov equation is constructed by using the modified (GG / G) -expansion method. Some new solutions are obtained, including hyperbolic function solution, trigonometric function solution, rational function solution and negative power solution.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175.29
本文编号：2166418
[Abstract]:(G / G) -expansion method is a powerful mathematical tool for constructing exact solutions of nonlinear evolution equations. In this paper, we discuss three equations. Firstly, the exact solution of the third order nonlinear wave equation is obtained by using the modified (GG / G) -expansion method. Secondly, the fractional nonlinear evolution equation is transformed into the nonlinear ordinary differential equation by using the fractional complex transformation. The exact solution of the nonlinear fractional Klein-Gordon equation is obtained by using the extended (G / G) -expansion method, and finally, the exact solution of the fractional modified Zakharov-Kuznetsov equation is constructed by using the modified (GG / G) -expansion method. Some new solutions are obtained, including hyperbolic function solution, trigonometric function solution, rational function solution and negative power solution.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175.29
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