共查询到20条相似文献,搜索用时 0 毫秒
1.
In this paper, a new special ansatz solution, where elliptic
equation satisfied by elliptic functions is taken as an
intermediate transformation, is applied to solve the
KdV-Burgers-Kuramoto equation, and many more new periodic
solutions are obtained, including solutions expressed in terms of
Jacobi elliptic functions, solution expressed in terms of
Weierstrass elliptic function. 相似文献
2.
In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained. 相似文献
3.
In this paper, by applying the extended Jacobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained. 相似文献
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The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions. 相似文献
6.
用改进的打靶法求解零温简谐势阱中中性原子玻色-爱因斯坦凝聚的一维Gross-Pitaevskii方程,给出不同非线性参数时凝聚体基态的本征值.用辛算法研究三个凝聚体在撤掉陷俘势后产生的干涉,和三个凝聚体处于同-陷俘势中的干涉及周期性演化,讨论不同的相对相位对凝聚体干涉的影响. 相似文献
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Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong. 相似文献
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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
12.
MEI Jian-Qin ZHANG Hong-Qing 《理论物理通讯》2005,44(8)
By using a new generally projective Riccati equation method and with the help of symbolic computation,we consider a nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. As a result,some new soliton solutions, rational function solution, and periodic solutions are obtained. 相似文献
13.
FU Zun-Tao LIU Shi-Kuo LIU Shi-Da 《理论物理通讯》2004,42(9)
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on. 相似文献
14.
A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well-known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values. 相似文献
15.
New Families of Soliton and Periodic Solutions of Bose-Einstein Condensation in Linear Magnetic Field and Time-Dependent Laser Field 总被引:1,自引:0,他引:1
MEI Jian-Qin ZHANG Hong-Qing 《理论物理通讯》2005,44(2):209-212
By using a new generally projective Riccati equation method and with the help of symbolic computation,we consider a nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. As a result,some new soliton solutions, rational function solution, and periodic solutions are obtained. 相似文献
16.
Elliptic Equation and New Solutions to Nonlinear Wave Equations 总被引:2,自引:0,他引:2
FUZun-Tao LIUShi-Kuo LIUShi-Da 《理论物理通讯》2004,42(3):343-346
The new solutions to elliptic equation are shown, and then the elliptic: equation is taken as a transformation and is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on. 相似文献
17.
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
18.
In this paper, based on the forms and structures of Wronskian solutions to soliton equations, a Wronskian form expansion method is presented to find a new class of interaction solutions to the Kadomtsev-Petviashvili equation. One characteristic of the method is that Wronskian entries do not satisfy linear partial differential equation. 相似文献
19.
The two-dimensional (2D) nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic
potential vorticity equation, can be investigated through the exact periodic-wave solutions for the Petviashvili equation, while the exact analytical periodic-wave solutions to the
Petviashvili equation are obtained by using the Jacobi elliptic function expansion method. It is shown that periodic-wave 2D Rossby solutions can be obtained by this method, and in the limit cases, the 2D Rossby soliton solutions are also obtained. 相似文献
20.
In this paper, based on the forms and structures of Wronskian solutions to soliton equations, a Wronskian form expansion method is presented to find a new class of interaction solutions to the Kadomtsev-Petviashvili equation. One characteristic of the method is that Wronskian entries do not satisfy linear partial differential equation. 相似文献