共查询到20条相似文献,搜索用时 31 毫秒
1.
The (3+1)-dimensional Jimbo-Miwa (JM)
equation is solved approximately by using the conformal invariant
asymptotic expansion approach presented by Ruan. By solving the new
(3+1)-dimensional integrable models, which are conformal invariant
and possess Painlevé property, the approximate solutions are
obtained for the JM equation, containing not only one-soliton
solutions but also periodic solutions and multi-soliton solutions.
Some approximate solutions happen to be exact and some approximate
solutions can become exact by choosing relations between the parameters properly. 相似文献
2.
3.
由于两自由度带电耦合振子系统的Lagrange函数中存在耦合项,从而导致其运动微分方程是非线性耦合的.先通过坐标变换消去Lagrange函数中的耦合项,用直接积分法求得系统的守恒量,用Adomian分解法求得系统的近似解,再通过坐标反变换求得系统在原坐标下的守恒量与近似解,并对近似解作了讨论. 相似文献
4.
YAO Ruo-Xia JIAO Xiao-Yu LOU Sen-Yue 《理论物理通讯》2009,51(5):785-788
Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky (KS) equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here. 相似文献
5.
This paper is devoted to the development of a novel approximate and numerical method for the solutions of linear and non-linear oscillatory systems, which are common in engineering dynamics. The original physical information included in the governing equations of motion is mostly transferred into the approximate and numerical solutions. Therefore, the approximate and numerical solutions generated by the present method reflect more accurately the characteristics of the motion of the systems. Furthermore, the solutions derived are continuous everywhere with good accuracy and convergence in comparing with Runge-Kutta method. An approximate solution is developed for a linear oscillatory problem and compared with its corresponding exact solution. A non-linear oscillatory problem is also solved numerically and compared with the solutions of Runge-Kutta method. Both the graphical and numerical comparisons are provided in the paper. The accuracy of the approximate and numerical solutions can be controlled as desired by the number of terms in the Taylor series and the value of a single parameter used in the present work. Formulae for numerical computation in solving various linear and non-linear oscillatory problems by the new approach are provided in the paper. 相似文献
6.
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method. 相似文献
7.
Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method 下载免费PDF全文
<正>This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method.Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders,showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method.The homotopy series solutions to the generalized Kawahara equation are consequently derived. 相似文献
8.
9.
Optical beams in lossy non-local Kerr media 总被引:1,自引:0,他引:1
It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions. 相似文献
10.
Mehmet Senol 《理论物理通讯》2020,72(5):55003-31
In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations. 相似文献
11.
LIU Xi-Zhong 《理论物理通讯》2010,54(1):31-34
The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered. 相似文献
12.
LIU Xi-Zhong 《理论物理通讯》2010,54(5):797-802
The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions of different orders are obtained for both methods, series reduction solutions are consequently derived. Higher order similarity reduction equations are linear variable coefficients ordinary differential equations. By comparison, it is find that the results generated from the approximate direct method are more general than the results generated from the approximate symmetry perturbation method. 相似文献
13.
Exact solutions of Gaussian solitons in nonlinear media with a
Gaussian nonlocal response are obtained. Using the variational
approach, we obtain the approximate solutions of such solitons when
the degree of the nonlocality is arbitrary. Specifically, we study
the conditions for Gaussian solitons that propagate in weakly
and highly nonlocal media. We also compare the variational result
with the known exact solutions for weakly and highly nonlocal media. 相似文献
14.
Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations 下载免费PDF全文
In this paper, we prove the convergence of homotopy analysis method (HAM).
We also apply the homotopy analysis method to obtain approximate
analytical solutions of systems of the second kind Volterra integral equations.
The HAM solutions contain an auxiliary parameter
which provides a convenient way of controlling the convergence region
of series solutions. It is shown that the solutions obtained by the
homotopy-perturbation method (HPM) are only special cases of the HAM
solutions. Several examples are given to illustrate
the efficiency and implementation of the method. 相似文献
15.
利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明,同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展, 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.
关键词:
同伦分析法
改进的 Zakharov-Kuznetsov方程
周期解 相似文献
16.
We propose an approximate method to obtain the speed of wavefronts. It is built up from a known variational principle. For a range of systems of biological and physical interest, comparison to previously-known solutions and to numerical simulations shows the powerfulness of our approximate technique. For time-delayed equations, we also propose an alternative approximate solution, based on the renormalization group approach, and we compare both approximations. 相似文献
17.
M. J. Englefield 《Journal of statistical physics》1988,52(1-2):369-381
Exact explicit solutions are given for a one-dimensional Fokker-Planck equation with a particular potential form involving hyperbolic functions. This potential contains four arbitrary parameters that can be chosen so that the potential is bistable. The solutions also contain parameters that can be chosen so that the initial distribution is approximately Gaussian, centered either at the unstable potential maximum or in the neighborhood of the secondary minimum. The use of the solutions to approximate solutions for other potentials is considered. 相似文献
18.
Retrieval of spheroidal particle size distribution using an approximate method in spectral extinction technique is proposed. The combined approximate method, which is the combination of Mie method and generalized eikonal approximation (GEA) method, is used as an alternative to the rigorous solutions to calculate the averaging extinction efficiency of spheroid. Based on the averaging extinction efficiency, the accuracy and limitations of the retrieval are then investigated. Moreover, the validity range and effect of the refractive index are also examined. The Johnson's SB function in this paper is used as a versatile function to fit the commonly used particle size distribution functions in the dependent model. Simulations and experimental results show that the combined approximate method can be successfully applied to retrieval of spheroidal particle size distribution. In certain constraint conditions, the retrieval results demonstrate the high reliability and stability of the method. By using the combined approximate method, the complexity and computation time of the retrieval are significantly reduced, which is more suitable for quick and easy measurement. The method can also be used as a replacement when the rigorous solutions suffer computationally intractable difficulties. 相似文献
19.
The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions. 相似文献