The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.展开更多
In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated ...In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated synchronization, and generalized synchronization. The presented scheme is used to investigate the generalized-type synchronization of the 4D hyperchaotic oscillator and the hyperchaotic oscillator with gyrators. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme is more powerful than the scalar signal scheme due to Grassi and Mascolo.展开更多
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into ano...Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.展开更多
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed b...Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.展开更多
By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial dif...By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.展开更多
The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propos...The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propose the greedy genetic algorithm which incorporates the global exploring ability of the genetic algorithm and the local convergent ability of the greedy algorithm. Experimental results show that greedy genetic algorithm gives much better results than the classical genetic algorithm.展开更多
In this paper we study linear secret sharing schemes by monotone span programs, according to the relation between realizing access structures by linear secret sharing schemes and computing monotone Boolean functions b...In this paper we study linear secret sharing schemes by monotone span programs, according to the relation between realizing access structures by linear secret sharing schemes and computing monotone Boolean functions by monotone span programs. We construct some linear secret sharing schemes. Furthermore, we study the rearrangements of access structures that is very important in practice.展开更多
Let F be a field of characteristic zero. W_n = F[t_1^(+-1), t_2^(+-1), ...,t_n^(+-1)] (partial deriv)/((partial deriv)t_1) + ... + F[t_1^(+-1), t_2^(+-1), ..., t_n^(+-1)](partial deriv)/((partial deriv)t_n) is the Wit...Let F be a field of characteristic zero. W_n = F[t_1^(+-1), t_2^(+-1), ...,t_n^(+-1)] (partial deriv)/((partial deriv)t_1) + ... + F[t_1^(+-1), t_2^(+-1), ..., t_n^(+-1)](partial deriv)/((partial deriv)t_n) is the Witt algebra over F, W_n^+ = F[t_1, t_2 ..., t_n](partial deriv)/((partial deriv)t_1) + ... + F[t_1, t_2 ..., t_n] (partial deriv)/((partialderiv)t_n) is Lie subalgebra of W_n. It is well known both W_n and W_n^+ are simple infinitedimensional Lie algebra. In Zhao's paper, it was conjectured that End(W_n^+) - {0} = Aut(W_n^+) andit was proved that the validity of this conjecture implies the validity of the well-known Jacobianconjecture. In this short note, we check the conjecture above for n = 1. We show End(W_1^+) - {0} =Aut(W_1^+).展开更多
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
文摘In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated synchronization, and generalized synchronization. The presented scheme is used to investigate the generalized-type synchronization of the 4D hyperchaotic oscillator and the hyperchaotic oscillator with gyrators. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme is more powerful than the scalar signal scheme due to Grassi and Mascolo.
基金National Key Basic Research Project of China under，国家自然科学基金，教育部留学回国人员科研启动基金
文摘Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.
文摘Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
文摘By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.
文摘The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propose the greedy genetic algorithm which incorporates the global exploring ability of the genetic algorithm and the local convergent ability of the greedy algorithm. Experimental results show that greedy genetic algorithm gives much better results than the classical genetic algorithm.
文摘In this paper we study linear secret sharing schemes by monotone span programs, according to the relation between realizing access structures by linear secret sharing schemes and computing monotone Boolean functions by monotone span programs. We construct some linear secret sharing schemes. Furthermore, we study the rearrangements of access structures that is very important in practice.
文摘Let F be a field of characteristic zero. W_n = F[t_1^(+-1), t_2^(+-1), ...,t_n^(+-1)] (partial deriv)/((partial deriv)t_1) + ... + F[t_1^(+-1), t_2^(+-1), ..., t_n^(+-1)](partial deriv)/((partial deriv)t_n) is the Witt algebra over F, W_n^+ = F[t_1, t_2 ..., t_n](partial deriv)/((partial deriv)t_1) + ... + F[t_1, t_2 ..., t_n] (partial deriv)/((partialderiv)t_n) is Lie subalgebra of W_n. It is well known both W_n and W_n^+ are simple infinitedimensional Lie algebra. In Zhao's paper, it was conjectured that End(W_n^+) - {0} = Aut(W_n^+) andit was proved that the validity of this conjecture implies the validity of the well-known Jacobianconjecture. In this short note, we check the conjecture above for n = 1. We show End(W_1^+) - {0} =Aut(W_1^+).
