By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other ...By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.展开更多
The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equa-tion and constructing new ansatz solution of the considered equation.As its application,the (2+1)-dimensionalKonopelch...The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equa-tion and constructing new ansatz solution of the considered equation.As its application,the (2+1)-dimensionalKonopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtainedincluding solitary wave solutions,trigonometric function solutions and Jacobi elliptic doubly periodic function solutions,some of which are new exact solutions that we have never seen before within our knowledge.The method can be appliedto other nonlinear evolution equations in mathematical physics.展开更多
A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lo...A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra.展开更多
In the current paper, based on fractional complex transformation, the GG2-expansion method which is used to solve differential equations of integer order is developed for finding exact solutions of nonlinear fractiona...In the current paper, based on fractional complex transformation, the GG2-expansion method which is used to solve differential equations of integer order is developed for finding exact solutions of nonlinear fractional differential equations with Jumarie's modified Riemann-Liouville derivative. And then, time-fractional Burgers equation and space-fractional coupled Konopelchenko-Dubrovsky equations are provided to show that this method is effective in solving nonlinear fractional differential equations.展开更多
基金Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)Supported by the Natural Science Foundation of Henan Province(0111050200)
文摘By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.
基金supported by the National Natural Science Foundation of China under Grant No.10672053the Scientific Research Fund of the Education Department of Hunan Province under Grant No.07D064
文摘The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equa-tion and constructing new ansatz solution of the considered equation.As its application,the (2+1)-dimensionalKonopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtainedincluding solitary wave solutions,trigonometric function solutions and Jacobi elliptic doubly periodic function solutions,some of which are new exact solutions that we have never seen before within our knowledge.The method can be appliedto other nonlinear evolution equations in mathematical physics.
基金浙江省自然科学基金，浙江省宁波市博士基金，the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation，Scientific Research Fund of Education Department of Zhejiang Province under
文摘A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra.
基金Supported by the National Natural Science Foundation of China（11462019） Supported by the Scientific Research Foundation of Inner Mongolia University for Nationalities（NMDYB1750, NMDGP1713）
文摘In the current paper, based on fractional complex transformation, the GG2-expansion method which is used to solve differential equations of integer order is developed for finding exact solutions of nonlinear fractional differential equations with Jumarie's modified Riemann-Liouville derivative. And then, time-fractional Burgers equation and space-fractional coupled Konopelchenko-Dubrovsky equations are provided to show that this method is effective in solving nonlinear fractional differential equations.
