In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the c...In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
Some new exact solutions of the Burgers-Fisher equation and generalized Burgers-Fisher equation have been obtained by using the first integral method. These solutions include exponential function solutions, singular s...Some new exact solutions of the Burgers-Fisher equation and generalized Burgers-Fisher equation have been obtained by using the first integral method. These solutions include exponential function solutions, singular solitary wave solutions and some more complex solutions whose figures are given in the article. The result shows that the first integral method is one of the most effective approaches to obtain the solutions of the nonlinear partial differential equations.展开更多
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation （ODE） method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bo...In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation （ODE） method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.展开更多
In this article, we apply five different techniques, namely the （G//G）-expansion method, an auxiliary equation method, the modified simple equation method, the first integral method and the Riccati equation method f...In this article, we apply five different techniques, namely the （G//G）-expansion method, an auxiliary equation method, the modified simple equation method, the first integral method and the Riccati equation method for constructing many new exact solutions with parameters as well as the bright-dark, singular and other soliton solutions of the （2＋1）-dimensional nonlinear cubic-quintic Ginzburg-Landau equation. Comparing the solutions of this nonlinear equation together with each other are presented. Comparing our new results obtained in this article with the well-known results are given too.展开更多
文摘In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
文摘Some new exact solutions of the Burgers-Fisher equation and generalized Burgers-Fisher equation have been obtained by using the first integral method. These solutions include exponential function solutions, singular solitary wave solutions and some more complex solutions whose figures are given in the article. The result shows that the first integral method is one of the most effective approaches to obtain the solutions of the nonlinear partial differential equations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10571110)the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2009AM011 and ZR2010AZ003)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103705110003)
文摘In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation （ODE） method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.
文摘In this article, we apply five different techniques, namely the （G//G）-expansion method, an auxiliary equation method, the modified simple equation method, the first integral method and the Riccati equation method for constructing many new exact solutions with parameters as well as the bright-dark, singular and other soliton solutions of the （2＋1）-dimensional nonlinear cubic-quintic Ginzburg-Landau equation. Comparing the solutions of this nonlinear equation together with each other are presented. Comparing our new results obtained in this article with the well-known results are given too.
