In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and othe...In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.展开更多
We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obt...We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.展开更多
A new modeling tool, algebraic state space approach to logical dynamic systems, which is developed recently based on the theory of semi-tensor product of matrices （STP）, is applied to the automata field. Using the S...A new modeling tool, algebraic state space approach to logical dynamic systems, which is developed recently based on the theory of semi-tensor product of matrices （STP）, is applied to the automata field. Using the STE this paper investigates the modeling and controlling problems of combined automata constructed in the ways of parallel, serial and feedback. By representing the states, input and output symbols in vector forms, the transition and output functions are expressed as algebraic equations of the states and inputs. Based on such algebraic descriptions, the control problems of combined automata, including output control and state control, are considered, and two necessary and sufficient conditions are presented for the controllability, by which two algorithms are established to find out all the control strings that make a combined automaton go to a target state or produce a desired output. The results are quite different from existing methods and provide a new angle and means to understand and analyze the dynamics of combined automata.展开更多
基金The project supported by National Natural Science Foundation of China, the Natural Science Foundation of Shandong Province of China, and the Natural Science Foundation of Liaocheng University .
文摘In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.
文摘We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.
基金Acknowledgements This work was supported by Key Scientific Research Program of the Higher Education Institutions of Henan Educational Committee （15A416005）, the 2015 Science Foundation of Henan University of Science and Technology for Youths （2015QN016）, and the National Natural Science Foundation of China （Grant Nos. 61573199, 61473115, and U1404610）. The authors would like to express their thanks to Prof. Y G Hong for his helpful suggestions.
文摘A new modeling tool, algebraic state space approach to logical dynamic systems, which is developed recently based on the theory of semi-tensor product of matrices （STP）, is applied to the automata field. Using the STE this paper investigates the modeling and controlling problems of combined automata constructed in the ways of parallel, serial and feedback. By representing the states, input and output symbols in vector forms, the transition and output functions are expressed as algebraic equations of the states and inputs. Based on such algebraic descriptions, the control problems of combined automata, including output control and state control, are considered, and two necessary and sufficient conditions are presented for the controllability, by which two algorithms are established to find out all the control strings that make a combined automaton go to a target state or produce a desired output. The results are quite different from existing methods and provide a new angle and means to understand and analyze the dynamics of combined automata.
