<正> We present a Darboux transformation for Tzitzeica equation associated with 3×3 matrix spectral problem.The explicit sohltion of Tzitzeica eqnation is obtained.
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
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
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
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
文摘概括有条件的对称被开发为类型 u_(xt ) 的方程学习可变分离 = A (u， u_x )u_(x x )+ B (u， u_x ) 。承认导出依赖者的功能的可分离的答案的那些方程的完全的分类被获得，一些他们的准确可分离的答案被构造。
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<正> We present a Darboux transformation for Tzitzeica equation associated with 3×3 matrix spectral problem.The explicit sohltion of Tzitzeica eqnation 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 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.
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.
