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Hongqing Zhang - One of the best experts on this subject based on the ideXlab platform.
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A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation
Journal of Applied Mathematics, 2012Co-Authors: Yafeng Xiao, Haili Xue, Hongqing ZhangAbstract:With the aid of symbolic computation, a new extended Jacobi Elliptic Function expansion method is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi Elliptic Functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi Elliptic Function solutions of nonlinear partial differential equations. As an application of the method, we choose the generalized shallow water wave (GSWW) equation to illustrate the method. As a result, we can successfully obtain more new solutions. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
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Discrete Jacobi Elliptic Function expansion method for nonlinear differential-difference equations
Physica Scripta, 2009Co-Authors: Hongqing ZhangAbstract:In this paper, an improved algorithm is devised to derive exact travelling wave solutions of nonlinear differential-difference equations (DDEs) by means of Jacobi Elliptic Functions. With the aid of symbolic computation, we choose the integrable discrete nonlinear Schrodinger equation to illustrate the validity and advantages of the method. As a result, new and more general Jacobi Elliptic Function solutions are obtained, from which hyperbolic Function solutions and trigonometric Function solutions are derived when the modulus m→1 and 0. It is shown that the proposed method provides a more effective mathematical tool for nonlinear DDEs in mathematical physics.
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The extension of the Jacobi Elliptic Function rational expansion method
Communications in Nonlinear Science and Numerical Simulation, 2007Co-Authors: Qi Wang, Hongqing ZhangAbstract:Abstract Using a new ansatz, we extend the Jacobi Elliptic Function rational expansion method and apply it to the asymmetric Nizhnik–Novikov–Veselov equations and the Davey–Stewartson equations. With the aid of symbolic computation, we construct more new Jacobi Elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular Functional (singly periodic) solutions.
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improved Jacobi Function method with symbolic computation to construct new double periodic solutions for the generalized ito system
Chaos Solitons & Fractals, 2006Co-Authors: Hongyan Zhi, Xueqin Zhao, Hongqing ZhangAbstract:Abstract The generalized Jacobi Elliptic Function method is further improved by picking up an Elliptic equation’s new solutions and introducing a general ansatz. It is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). As an application of the method, we choose the generalized Ito system to illustrate the method. The solitary wave solutions and triangular periodic solutions can be obtained at their limit condition.
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a generalized f expansion method to find abundant families of Jacobi Elliptic Function solutions of the 2 1 dimensional nizhnik novikov veselov equation
Chaos Solitons & Fractals, 2006Co-Authors: Hongqing ZhangAbstract:Abstract In the present paper, a generalized F-expansion method is proposed by further studying the famous extended F-expansion method and using a generalized transformation to seek more types of solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose (2 + 1)-dimensional Nizhnik–Novikov–Veselov equations to illustrate the validity and advantages of the method. As a result, abundant new exact solutions are obtained including Jacobi Elliptic Function solutions, soliton-like solutions, trigonometric Function solution etc. The method can be also applied to other nonlinear partial differential equations.
Qi Wang - One of the best experts on this subject based on the ideXlab platform.
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The extension of the Jacobi Elliptic Function rational expansion method
Communications in Nonlinear Science and Numerical Simulation, 2007Co-Authors: Qi Wang, Hongqing ZhangAbstract:Abstract Using a new ansatz, we extend the Jacobi Elliptic Function rational expansion method and apply it to the asymmetric Nizhnik–Novikov–Veselov equations and the Davey–Stewartson equations. With the aid of symbolic computation, we construct more new Jacobi Elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular Functional (singly periodic) solutions.
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the extended Jacobi Elliptic Function method to solve a generalized hirota satsuma coupled kdv equations
Chaos Solitons & Fractals, 2005Co-Authors: Qi Wang, Hongqing ZhangAbstract:Abstract In this paper, we extend the Jacobi Elliptic Function rational expansion method by using a new generalized ansatz. With the help of symbolic computation, we construct more new explicit exact solutions of nonlinear evolution equations (NLEEs). We apply this method to a generalized Hirota–Satsuma coupled KdV equations and gain more general solutions. The general solutions not only contain the solutions by the existing Jacobi Elliptic Function expansion methods but also contain many new solutions. When the modulus of the Jacobi Elliptic Functions m → 1 or 0, the corresponding solitary wave solutions and triangular Functional (singly periodic) solutions are also obtained.
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an extended Jacobi Elliptic Function rational expansion method and its application to 2 1 dimensional dispersive long wave equation
Physics Letters A, 2005Co-Authors: Yong Chen, Qi Wang, Hongqing ZhangAbstract:With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi Elliptic Functions, is more powerful than exiting Jacobi Elliptic Function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi Elliptic Function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
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extended Jacobi Elliptic Function rational expansion method and abundant families of Jacobi Elliptic Function solutions to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi WangAbstract:Abstract Our Jacobi Elliptic Function rational expansion method is extended to be a more powerful method, called the extended Jacobi Elliptic Function rational expansion method, by using more general ansatz. The (1 + 1)-dimensional dispersive long wave equation is chosen to illustrate the approach. As a consequence, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. When the modulus m → 1, these doubly periodic solutions degenerate as soliton solutions. The method can be also applied to other nonlinear differential equations.
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a new Jacobi Elliptic Function rational expansion method and its application to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi Wang, Zhang HongqingAbstract:Abstract With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz and is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). As an application of the method, we choose a (1 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
Zhang Hongqing - One of the best experts on this subject based on the ideXlab platform.
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extended Jacobi Elliptic Function rational expansion method and its application to 2 1 dimensional stochastic dispersive long wave system
Communications in Theoretical Physics, 2007Co-Authors: Song Lina, Zhang HongqingAbstract:In this work, by means of a generalized method and symbolic computation, we extend the Jacobi Elliptic Function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi Elliptic Function solutions.
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construction of doubly periodic solutions to nonlinear partial differential equations using improved Jacobi Elliptic Function expansion method and symbolic computation
Chinese Physics, 2006Co-Authors: Zhi Hongyan, Zhao Xueqin, Zhang HongqingAbstract:Some doubly-periodic solutions of the Zakharov?Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi Elliptic Function solutions to construct doubly-periodic solutions of the Zakharov?Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k?1, these solutions reduce to the solitary wave solutions of the equation.
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further extended Jacobi Elliptic Function rational expansion method and new families of Jacobi Elliptic Function solutions to 2 1 dimensional dispersive long wave equation
Communications in Theoretical Physics, 2006Co-Authors: Zhang Yuanyuan, Zhang HongqingAbstract:In this paper, a further extended Jacobi Elliptic Function rational expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to (2+1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these solutions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.
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a new Jacobi Elliptic Function rational expansion method and its application to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi Wang, Zhang HongqingAbstract:Abstract With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz and is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). As an application of the method, we choose a (1 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
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a new Jacobi Elliptic Function rational expansion method and its application to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi Wang, Zhang HongqingAbstract:Abstract With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz and is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). As an application of the method, we choose a (1 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
Yong Chen - One of the best experts on this subject based on the ideXlab platform.
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an extended Jacobi Elliptic Function rational expansion method and its application to 2 1 dimensional dispersive long wave equation
Physics Letters A, 2005Co-Authors: Yong Chen, Qi Wang, Hongqing ZhangAbstract:With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi Elliptic Functions, is more powerful than exiting Jacobi Elliptic Function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi Elliptic Function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
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extended Jacobi Elliptic Function rational expansion method and abundant families of Jacobi Elliptic Function solutions to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi WangAbstract:Abstract Our Jacobi Elliptic Function rational expansion method is extended to be a more powerful method, called the extended Jacobi Elliptic Function rational expansion method, by using more general ansatz. The (1 + 1)-dimensional dispersive long wave equation is chosen to illustrate the approach. As a consequence, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. When the modulus m → 1, these doubly periodic solutions degenerate as soliton solutions. The method can be also applied to other nonlinear differential equations.
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a new Jacobi Elliptic Function rational expansion method and its application to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi Wang, Zhang HongqingAbstract:Abstract With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz and is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). As an application of the method, we choose a (1 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
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a new Jacobi Elliptic Function rational expansion method and its application to 1 1 dimensional dispersive long wave equation
Chaos Solitons & Fractals, 2005Co-Authors: Yong Chen, Qi Wang, Zhang HongqingAbstract:Abstract With the aid of computerized symbolic computation, a new Elliptic Function rational expansion method is presented by means of a new general ansatz and is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). As an application of the method, we choose a (1 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi Elliptic Function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.
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Jacobi Elliptic Function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations
Zeitschrift für Naturforschung A, 2004Co-Authors: Yong Chen, Qi Wang, Biao LicAbstract:A new Jacobi Elliptic Function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi Elliptic Function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi Elliptic Function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi Elliptic Functions m → 1 or 0, the corresponding solitary wave solutions and trigonometric Function (singly periodic) solutions are also found.
Zhenya Yan - One of the best experts on this subject based on the ideXlab platform.
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Approximate Jacobi Elliptic Function solutions of the modified KdV equation via the decomposition method
Applied Mathematics and Computation, 2005Co-Authors: Zhenya YanAbstract:The scheme is developed to obtain approximate Jacobi Elliptic Function solutions of the modified KdV equation with initial conditions via the Adomian decomposition method. As consequence, we derive the approximate solution and exact Jacobi Elliptic Function solutions of the modified KdV equation with initial conditions. The approximate solution is compared with the exact solution. Moreover we analyze the absolute error and relative error, and give the contour and density plots of the approximate Jacobi Elliptic Function solutions with different modulus m=0.25,0.5,1.
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abundant families of Jacobi Elliptic Function solutions of the 2 1 dimensional integrable davey stewartson type equation via a new method
Chaos Solitons & Fractals, 2003Co-Authors: Zhenya YanAbstract:Our extended Jacobi Elliptic Function expansion method is further improved to be a more powerful method, which is still called the extended Jacobi Elliptic Function expansion method, by using 12 Jacobi Elliptic Functions. The new (2+1)-dimensional integrable Davey–Stewartson-type is chosen to illustrate the approach. As a consequence, 24 families of Jacobi Elliptic Function solutions are obtained. When the modulus m→1, these doubly periodic solutions degenerate as soliton solutions. The method can be also applied to other nonlinear differential equations.
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new Jacobi Elliptic Function solutions of 2 1 dimensional complex nonlinear integrable system
International Journal of Modern Physics C, 2003Co-Authors: Zhenya YanAbstract:Recently sixteen types of doubly-periodic solutions were obtained for the new (2 +1)-dimensional complex nonlinear integrable system. In this paper with the aid of computerized symbolic computation, our extended Jacobi Elliptic Function expansion method is extended to this system. As a result, another eight families of Jacobian Elliptic Functions solutions are also found.
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Modified nonlinearly dispersive mK(m,n,k) equations: II. Jacobi Elliptic Function solutions
Computer Physics Communications, 2003Co-Authors: Zhenya YanAbstract:Abstract Recently we have obtained compacton solutions and solitary pattern solutions of the modified nonlinearly dispersive KdV equations (simply called mK(m,n,k) equations). In this paper the mK(m,n,k) equations are investigated again. By using some transformations we give their some Jacobi Elliptic Function solutions. When the modulus μ→1 or 0, some of the obtained Jacobi Elliptic Function solutions degenerate as solitary wave solution.