In this paper, exact solutions are derived for four coupled complex nonlinear different equations by using simplified transformation method and algebraic equations.
In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is mo...In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.展开更多
The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In t...The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.展开更多
In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on comp...In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.展开更多
In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex trans...In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.展开更多
With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnecte...With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics.The corresponding exact solution suitable for arbitrary boundary conditions is presented.Furthermore,the methodology for computing the coefficients of the modal shape function is proposed.As an example,the explicit expression of the modal shape function is derived,provided only one damper is adopted to connect the adjacent buildings.Finally,to validate the proposed methodologies,three case studies are performed,in which the existence of the overdamping and the optimal damping coefficient are revealed.In the case of using one damper in connecting two similar buildings,the estimating equations for the first modal damping ratio are formulated.展开更多
With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ ...With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ my ＋ nt ＋ Г（x,y, t） for the （2＋1）-dimensional generalized Calogero-Bogoyavlenskii-Schiff system （GCBS） are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.展开更多
In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real...In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.展开更多
In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth...In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.展开更多
Dierential geometry play a fundamental role in discussing partial dierential equations（PDEs） in mathematical physics. Recently discrete dierential geometry is an active mathematical terrain, which aims at the develo...Dierential geometry play a fundamental role in discussing partial dierential equations（PDEs） in mathematical physics. Recently discrete dierential geometry is an active mathematical terrain, which aims at the development and application of discrete equivalents of the geometric notions and methods of dierential geometry. In this paper, a discrete theory of exterior dierential calculus and the analogue of the Poincar′e lemma for dierential-dierence complex are proposed. They provide an intrinsic idea for developing the theory to discuss the integrability of dierence equations.展开更多
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function s...Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.展开更多
文摘In this paper, exact solutions are derived for four coupled complex nonlinear different equations by using simplified transformation method and algebraic equations.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.
基金Supported in part by the Basic Science and the Front Technology Research Foundation of Henan Province of China under Grant No.092300410179the Doctoral Scientific Research Foundation of Henan University of Science and Technology under Grant No.09001204
文摘The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.
文摘In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.
文摘In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.
文摘With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics.The corresponding exact solution suitable for arbitrary boundary conditions is presented.Furthermore,the methodology for computing the coefficients of the modal shape function is proposed.As an example,the explicit expression of the modal shape function is derived,provided only one damper is adopted to connect the adjacent buildings.Finally,to validate the proposed methodologies,three case studies are performed,in which the existence of the overdamping and the optimal damping coefficient are revealed.In the case of using one damper in connecting two similar buildings,the estimating equations for the first modal damping ratio are formulated.
基金supported by the National Natural Science Foundation of China(Grant No.11375079)the Scientific Research Fund of Zhejiang Provincial Education Department of China(Grant No.Y 201120994)the Natural Science Foundation of Zhejiang Province,China(Grant Nos.Y6100257,LY14A010005,and Y6110140)
文摘With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ my ＋ nt ＋ Г（x,y, t） for the （2＋1）-dimensional generalized Calogero-Bogoyavlenskii-Schiff system （GCBS） are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.
文摘In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.
文摘In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.
文摘Dierential geometry play a fundamental role in discussing partial dierential equations（PDEs） in mathematical physics. Recently discrete dierential geometry is an active mathematical terrain, which aims at the development and application of discrete equivalents of the geometric notions and methods of dierential geometry. In this paper, a discrete theory of exterior dierential calculus and the analogue of the Poincar′e lemma for dierential-dierence complex are proposed. They provide an intrinsic idea for developing the theory to discuss the integrability of dierence equations.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. Y604106 and Y606181, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005 Acknowledgments The authors are in debt to Profs. J.P. Fang, H.P. Zhu, and J.F. Zhang, and Drs. Z.Y. Ma and W.H. Huang for their fruitful discussions.
文摘Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.
