This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It succes...This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.展开更多
In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10575082 and 10247008）.
文摘This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.
文摘In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
基金The National Natural Science Foundation of China(1116102711262009+3 种基金11226132)the Scientific Research Projects in Colleges and Universities of Gansu Province of China(2013A-043)the Fundamental Research Funds for the Universities of Gansu Province(212084)the Youth Science Foundation of Lanzhou Jiaotong University(2012019)
