一个新的广义射影Riccati方程展开法及其应用  

A new generalized projective riccati equation expansion method and its application

作　　者：刘娟[1] 张小中[1] 

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《河南理工大学学报（自然科学版）》2012年第6期753-756,共4页Journal of Henan Polytechnic University（Natural Science）

基　　金：国家青年科学基金资助项目(61104119);国家自然科学基金资助项目(41204035)

摘　　要：物理学方程,尤其是在流体力学、空气动力学、等离子体物理、生物物理和化学物理等现代科学技术中引出的非线性发展方程,其精确解有重大的理论和应用研究价值,许多数学家和物理学家为此作了大量工作.借助于符号计算软件Maple,通过利用一个新的更为广义的Ric-cati方程有理展开法,得到了非线性项具有任意次幂的非线性反应扩散方程的一些新的更广义的精确解.此方法还可以应用到其他的非线性发展方程中去.Many nonlinear evolution equations were arisen form physics equations, especially in the fluid me- chanics, aerodynamics, plasma physics, biology physical and chemical physical, etc. Because the precise so- lution is of great theoretical and applied research value, many mathematicians and physicists did a lot of work. In this paper, based upon a new generalized Projective Riccati equation rational expansion method, some new generalexact solutions are obtained for the single-nonlinear reaction-diffusion equation with nonlinear terms of arbitrary order. The presented method can also be applied to other nonlinear evolution equations with nonlinear terms of arbitrary order.

关 键 词：广义RICCATI方程 三角周期解 指数函数解 类孤子解 

分 类 号：TV139[水利工程—水力学及河流动力学]