The Experts below are selected from a list of 2061 Experts worldwide ranked by ideXlab platform
Zhenya Yan - One of the best experts on this subject based on the ideXlab platform.
-
the new extended Jacobian Elliptic Function expansion algorithm and its applications in nonlinear mathematical physics equations
Computer Physics Communications, 2003Co-Authors: Zhenya YanAbstract:More recently we have presented the extended Jacobian Elliptic Function expansion method and its algorithm to seek more types of doubly periodic solutions. Based on the idea of the method, by studying more relations among all twelve kinds of Jacobian Elliptic Functions. we further extend the method to be a more general method, which is still called the extended Jacobian Elliptic Function expansion method for convenience. The new method is more powerful to construct more new exact doubly periodic solutions of nonlinear equations. We choose the (2+1)-dimensional dispersive long-wave system to illustrate our algorithm. As a result, twenty-four families of new doubly periodic solutions are obtained. When the modulus m→1 or 0, these doubly periodic solutions degenerate as soliton solutions and trigonometric Function solutions. This algorithm can be also applied to other nonlinear equations.
-
jacobi Elliptic Function solutions of nonlinear wave equations via the new sinh gordon equation expansion method
Journal of Physics A, 2003Co-Authors: Zhenya YanAbstract:In this paper, based on the well-known sinh-Gordon equation, a new sinh-Gordon equation expansion method is developed. This method transforms the problem of solving nonlinear partial differential equations into the problem of solving the corresponding systems of algebraic equations. With the aid of symbolic computation, the procedure can be carried out by computer. Many nonlinear wave equations in mathematical physics are chosen to illustrate the method such as the KdV-mKdV equation, (2+1)-dimensional coupled Davey–Stewartson equation, the new integrable Davey–Stewartson-type equation, the modified Boussinesq equation, (2+1)-dimensional mKP equation and (2+1)-dimensional generalized KdV equation. As a consequence, many new doubly-periodic (Jacobian Elliptic Function) solutions are obtained. When the modulus m → 1 or 0, the corresponding solitary wave solutions and singly-periodic solutions are also found. This approach can also be applied to solve other nonlinear differential equations.
-
the extended Jacobian Elliptic Function expansion method and its application in the generalized hirota satsuma coupled kdv system
Chaos Solitons & Fractals, 2003Co-Authors: Zhenya YanAbstract:Abstract In this paper an extended Jacobian Elliptic Function expansion method, which is a direct and more powerful method, is used to construct more new exact doubly periodic solutions of the generalized Hirota–Satsuma coupled KdV system by using symbolic computation. As a result, sixteen families of new doubly periodic solutions are obtained which shows that the method is more powerful. When the modulus of the Jacobian Elliptic Functions m →1 or 0, the corresponding six solitary wave solutions and six trigonometric Function (singly periodic) solutions are also found. The method is also applied to other higher-dimensional nonlinear evolution equations in mathematical physics.
-
The extended Jacobian Elliptic Function expansion method and its application in the generalized Hirota–Satsuma coupled KdV system
Chaos Solitons & Fractals, 2003Co-Authors: Zhenya YanAbstract:Abstract In this paper an extended Jacobian Elliptic Function expansion method, which is a direct and more powerful method, is used to construct more new exact doubly periodic solutions of the generalized Hirota–Satsuma coupled KdV system by using symbolic computation. As a result, sixteen families of new doubly periodic solutions are obtained which shows that the method is more powerful. When the modulus of the Jacobian Elliptic Functions m →1 or 0, the corresponding six solitary wave solutions and six trigonometric Function (singly periodic) solutions are also found. The method is also applied to other higher-dimensional nonlinear evolution equations in mathematical physics.
-
extended Jacobian Elliptic Function algorithm with symbolic computation to construct new doubly periodic solutions of nonlinear differential equations
Computer Physics Communications, 2002Co-Authors: Zhenya YanAbstract:Abstract With the aid of computerized symbolic computation, the extended Jacobian Elliptic Function expansion method and its algorithm are presented by using some relations among ten Jacobian Elliptic Functions and are very powerful to construct more new exact doubly-periodic solutions of nonlinear differential equations in mathematical physics. The new (2+1)-dimensional complex nonlinear evolution equations is chosen to illustrate our algorithm such that sixteen families of new doubly-periodic solutions are obtained. When the modulus m →1 or 0, these doubly-periodic solutions degenerate as solitonic solutions including bright solitons, dark solitons, new solitons as well as trigonometric Function solutions.
Timoleon Crepin Kofane - One of the best experts on this subject based on the ideXlab platform.
-
Jacobian Elliptic Function solutions of the discrete cubic–quintic nonlinear Schrödinger equation
Journal of Physics A: Mathematical and Theoretical, 2007Co-Authors: G C Latchio Tiofack, Alidou Mohamadou, Timoleon Crepin KofaneAbstract:The study of solitary wave solutions is of prime significance for the nonlinear Schrodinger equation with higher order dispersion and/or higher degree nonlinearities in nonlinear physical systems. We derive the discrete cubic–quintic nonlinear Schrodinger equation from a Hamiltonian using different Poisson brackets. By using the extended Jacobian Elliptic Function approach, we investigate the abundant exact stationary solitons and periodic waves solution of this equation. These solutions include, Jacobian periodic solutions, alternating phase Jacobi periodic solution, kink and bubble soliton solutions, alternating phase kink soliton solution and alternating phase bubble soliton solution, provided that coefficients are bound by special relation. And then with the aid of symbolic computation, we present in explicit form these solutions. The stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated.
-
Jacobian Elliptic Function solutions of the discrete cubic quintic nonlinear schrodinger equation
Journal of Physics A, 2007Co-Authors: G C Latchio Tiofack, Alidou Mohamadou, Timoleon Crepin KofaneAbstract:The study of solitary wave solutions is of prime significance for the nonlinear Schrodinger equation with higher order dispersion and/or higher degree nonlinearities in nonlinear physical systems. We derive the discrete cubic–quintic nonlinear Schrodinger equation from a Hamiltonian using different Poisson brackets. By using the extended Jacobian Elliptic Function approach, we investigate the abundant exact stationary solitons and periodic waves solution of this equation. These solutions include, Jacobian periodic solutions, alternating phase Jacobi periodic solution, kink and bubble soliton solutions, alternating phase kink soliton solution and alternating phase bubble soliton solution, provided that coefficients are bound by special relation. And then with the aid of symbolic computation, we present in explicit form these solutions. The stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated.
A. Chakrabarti - One of the best experts on this subject based on the ideXlab platform.
-
A Generalization of $U_h(sl(2))$ via Jacobian Elliptic Function
arXiv: Quantum Algebra, 1996Co-Authors: A. ChakrabartiAbstract:A two-parametric generalization of the Jordanian deformation $U_h (sl(2))$ of $sl(2)$ is presented. This involves Jacobian Elliptic Functions. In our deformation $U_{(h,k)}(sl(2))$, for $k^2=1$ one gets back $U_h(sl(2))$. The constuction is presented via a nonlinear map on $sl(2)$. This invertible map directly furnishes the highest weight irreducible representations of $U_{(h,k)}(sl(2))$. This map also provides two distinct induced Hopf stuctures, which are exhibited. One is induced by the classical $sl(2)$ and the other by the distinct one of $U_h(sl(2))$. Automorphisms related to the two periods of the Elliptic Functions involved are constructed. Translations of one generator by half and quarter periods lead to interesting results in this context. Possibilities of applications are discussed briefly.
-
a generalization of u_h sl 2 via Jacobian Elliptic Function
arXiv: Quantum Algebra, 1996Co-Authors: A. ChakrabartiAbstract:A two-parametric generalization of the Jordanian deformation $U_h (sl(2))$ of $sl(2)$ is presented. This involves Jacobian Elliptic Functions. In our deformation $U_{(h,k)}(sl(2))$, for $k^2=1$ one gets back $U_h(sl(2))$. The constuction is presented via a nonlinear map on $sl(2)$. This invertible map directly furnishes the highest weight irreducible representations of $U_{(h,k)}(sl(2))$. This map also provides two distinct induced Hopf stuctures, which are exhibited. One is induced by the classical $sl(2)$ and the other by the distinct one of $U_h(sl(2))$. Automorphisms related to the two periods of the Elliptic Functions involved are constructed. Translations of one generator by half and quarter periods lead to interesting results in this context. Possibilities of applications are discussed briefly.
Alidou Mohamadou - One of the best experts on this subject based on the ideXlab platform.
-
Jacobian Elliptic Function solutions of the discrete cubic–quintic nonlinear Schrödinger equation
Journal of Physics A: Mathematical and Theoretical, 2007Co-Authors: G C Latchio Tiofack, Alidou Mohamadou, Timoleon Crepin KofaneAbstract:The study of solitary wave solutions is of prime significance for the nonlinear Schrodinger equation with higher order dispersion and/or higher degree nonlinearities in nonlinear physical systems. We derive the discrete cubic–quintic nonlinear Schrodinger equation from a Hamiltonian using different Poisson brackets. By using the extended Jacobian Elliptic Function approach, we investigate the abundant exact stationary solitons and periodic waves solution of this equation. These solutions include, Jacobian periodic solutions, alternating phase Jacobi periodic solution, kink and bubble soliton solutions, alternating phase kink soliton solution and alternating phase bubble soliton solution, provided that coefficients are bound by special relation. And then with the aid of symbolic computation, we present in explicit form these solutions. The stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated.
-
Jacobian Elliptic Function solutions of the discrete cubic quintic nonlinear schrodinger equation
Journal of Physics A, 2007Co-Authors: G C Latchio Tiofack, Alidou Mohamadou, Timoleon Crepin KofaneAbstract:The study of solitary wave solutions is of prime significance for the nonlinear Schrodinger equation with higher order dispersion and/or higher degree nonlinearities in nonlinear physical systems. We derive the discrete cubic–quintic nonlinear Schrodinger equation from a Hamiltonian using different Poisson brackets. By using the extended Jacobian Elliptic Function approach, we investigate the abundant exact stationary solitons and periodic waves solution of this equation. These solutions include, Jacobian periodic solutions, alternating phase Jacobi periodic solution, kink and bubble soliton solutions, alternating phase kink soliton solution and alternating phase bubble soliton solution, provided that coefficients are bound by special relation. And then with the aid of symbolic computation, we present in explicit form these solutions. The stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated.
Jeng Dong-sheng - One of the best experts on this subject based on the ideXlab platform.
-
Cnoidal wave induced seabed response around a buried pipeline
Elsevier, 2015Co-Authors: Zhou Xiang-lian, Zhang Jun, Cuo Jun-jie, Wang Jian-hua, Jeng Dong-shengAbstract:The evaluation of wave-induced pore pressures and effective stresses in a poroelastic seabed is important for coastal and ocean engineers in the design of marine structures. Most previous theoretical investigations have focused commonly on the Stokes wave induced seabed response. In this paper, a cnoidal wave–seabed–pipeline system is modeled using the finite element method. Taylor’s expression and the precise integration method are used to estimate the Jacobian Elliptic Function. The seabed is treated as a poroelastic medium and is characterized by Biot’s partly dynamic equations (u–p model). The pore water pressure and effective vertical stress on the poroelastic seabed around a buried pipeline are examined. Based on the numerical results, a parametric study is conducted to examine the effects of wave and seabed characteristics on the seabed response. Comparison with the cnodial wave and Stokes wave induced seabed response is also demonstrated here. It implies that the difference between the maximum pore pressure and vertical effective stress induced by the cnoidal wave and Stokes wave may reach 60–70%.No Full Tex
-
Stability and liquefaction analysis of porous seabed subjected to cnoidal wave
Pergamon Press, 2014Co-Authors: Xl Zhou, Zhang J, Wang J, Xu Y.-f., Jeng Dong-shengAbstract:Cnoidal wave theory is appropriate to periodic wave progressing in water whose depth is less than 1/10 wavelength. However, the cnoidal wave theory has not been widely applied in practical engineering because the formula for wave profile involves Jacobian Elliptic Function. In this paper, a cnoidal wave-seabed system is modeled and discussed in detail. The seabed is treated as porous medium and characterized by Biot's partly dynamic equations (u-p model). A simple and useful calculating technique for Jacobian Elliptic Function is presented. Upon specification of water depth, wave height and wave period, Taylor's expression and precise integration method are used to estimate Jacobian Elliptic Function and cnoidal wave pressure. Based on the numerical results, the effects of cnoidal wave and seabed characteristics, such as water depth, wave height, wave period, permeability, elastic modulus, and degree of saturation, on the cnoidal wave-induced excess pore pressure and liquefaction phenomenon are studied.No Full Tex
