The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and...The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and the recurrence and transience of underlying processes.展开更多
The generalized conditional symmetry is developed to study the variable separation for equations of type uxt = A（u,ux）uxx ＋ B（u, ux）. Complete classification of those equations which admit derivative-dependent fu...The generalized conditional symmetry is developed to study the variable separation for equations of type uxt = A（u,ux）uxx ＋ B（u, ux）. Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.展开更多
We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,
The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Konop...The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including 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 applied to other nonlinear evolution equations in mathematical physics.展开更多
In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended t...In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.展开更多
This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weie...This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.展开更多
A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate eq...A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly const...In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions＇ soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.展开更多
文摘The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and the recurrence and transience of underlying processes.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10371098, 10447007, aria 10475055, the Natural Science Foundation of Shaanxi Province of China under Grant No. 2005A13, and the Special Research Project of Educational Department of Shaanxi Province under Grant No. 03JK060
文摘The generalized conditional symmetry is developed to study the variable separation for equations of type uxt = A（u,ux）uxx ＋ B（u, ux）. Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.
基金The project supported by National Natural Science Foundation of China under Grant No. 10471132 and the Special Foundation for the State Key Basic Research Program ＂Nonlinear Sciencc＂
文摘We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,
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 generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including 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 applied to other nonlinear evolution equations in mathematical physics.
文摘In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.
基金supported by the Open Project of Key Laboratory of Mathematics Mechanization,CAS under Grant No.KLMM0602
文摘This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.
文摘A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
基金The author would like to thank the referees very much for their careful reading of the manuscript and many valuable suggestions.
文摘In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions＇ soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
