共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2 1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations. 相似文献
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ZHENG Ying ZHANG Yuan-Yuan ZHANG Hong-Qing 《理论物理通讯》2006,46(1):5-9
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2+1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations. 相似文献
3.
With the aid of computerized symbolic computation, an improved F-expansion method is presented to uniformly construct more new exact doubly periodic solutions in terms of rational formal Jacobi elliptic function of nonlinear partial differential equations (NPDEs). The coupled
Drinfel'd-Sokolov-Wilson equation is chosen to illustrate the method. As a
result, we can successfully obtain abundant new doubly periodic
solutions without calculating various Jacobi elliptic functions. In
the limit cases, the rational solitary wave solutions and trigonometric function solutions are obtained as well. 相似文献
4.
In this paper, new basic functions, which are composed of three
basic Jacobi elliptic functions, are chosen as components of
finite expansion. This finite expansion can be taken as an ansatz
and applied to solve nonlinear wave equations. As an example, mKdV
equation is solved, and more new rational form solutions are
derived, such as periodic solutions of rational form, solitary
wave solutions of rational form, and so on. 相似文献
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Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations 总被引:1,自引:0,他引:1
The Jacobi elliptic function expansion method is extended to derive the
explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are
chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi
elliptic cosine function and the third elliptic function solutions
are obtained. It is shown that the shock wave solutions and
solitary wave solutions can be obtained at their limit condition. 相似文献
6.
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. 相似文献
7.
DOU Fu-Quan SUN Jian-An DUAN Wen-Shan SHI Yu-Ren LÜ Ke-Pu HONG Xue-Ren 《理论物理通讯》2006,45(6):1063-1068
With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for
constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing
methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional
Kadomtsev-Petviashvili equation to illustrate our method. As a
result, twenty families of periodic solutions are obtained. Of
course, more solitary wave solutions, shock wave solutions or
triangular function formal solutions can be obtained at their limit
condition. 相似文献
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通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解.
关键词:
非线性发展方程
Jacobi椭圆函数
双周期解
行波解 相似文献
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LIU Shi-Kuo GAO Bin FU Zun-Tao LIU Shi-Da 《理论物理通讯》2009,51(6):1069-1072
In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained. 相似文献
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SONG Li-Na ZHANG Hong-Qing 《理论物理通讯》2007,47(6):969-974
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. 相似文献
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In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations.
With the aid of symbolic computation, we apply the proposed method
to solving the (1+1)-dimensional dispersive long wave equation and
explicitly construct a series of exact solutions which include the
rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases. 相似文献
20.
SHI Yun-Long YANG Hong-Wei YIN Bao-Shu YANG De-Zhou XU Zhen-Hua FENG Xing-Ru 《理论物理通讯》2015,64(4):464-472
The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves. 相似文献