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YU Ya-Xuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2005,44(6):1011-1014
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result, many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple. 相似文献
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YU Ya-Xuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2005,44(12)
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple. 相似文献
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研究了一类非线性燃烧模型.利用同伦分析方法,得到了该模型的近似解.
关键词:
非线性方程
燃烧模型
同伦分析法
近似解 相似文献
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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
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本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统,成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。 相似文献
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Approximate solution for the Klein-Gordon-SchrSdinger equation by the homotopy analysis method 下载免费PDF全文
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution. 相似文献
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In this paper, we introduce conformable variational iteration method (C-VIM), conformable fractional reduced differential transform method (CFRDTM) and conformable homotopy analysis method (C-HAM). Between these methods, the C-VIM is introduced for the first time for fractional partial differential equations (FPDEs). These methods are new versions of well-known VIM, RDTM and HAM. In addition, above-mentioned techniques are based on new defined conformable fractional derivative to solve linear and non-linear conformable FPDEs. Firstly, we present some basic definitions and general algorithm for proposal methods to solve linear and non-linear FPDEs. Secondly, to understand better, the presented new methods are supported by some examples. Finally, the obtained results are illustrated by the aid of graphics and the tables. The applications show that these new techniques C-VIM, CFRDTM and C-HAM are extremely reliable and highly accurate and it provides a significant improvement in solving linear and non-linear FPDEs. 相似文献
9.
A. Sami Bataineh 《Physics letters. A》2008,372(5):613-618
In this Letter, the homotopy analysis method (HAM) is employed to obtain a family of series solutions of the time-dependent reaction-diffusion problems. HAM provides a convenient way of controlling the convergence region and rate of the series solution. 相似文献
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Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap 下载免费PDF全文
<正>The Homotopy analysis method(HAM) is adopted to find the approximate analytical solutions of the GrossPitaevskii equation,a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they fit very well with each other when the atomic interaction is weak. 相似文献
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In this Letter we propose a new generalization of the two-dimensional differential transform method that will extend the application of the method to a diffusion-wave equation with space- and time-fractional derivatives. The new generalization is based on generalized Taylor's formula and Caputo fractional derivative. Theorems that are never existed before are introduced with their proofs. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The results reveal that the technique introduced here is very effective and convenient for solving partial differential equations of fractional order. 相似文献
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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
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LIU YanBin & CHEN YuShu School of Astronautics Harbin Institute of Technology China P.O.Box Harbin China 《中国科学:物理学 力学 天文学(英文版)》2011,(6)
The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also ana... 相似文献
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An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders,educing the related homotopy series solutions.Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation.Higher order similarity solutions can be obtained by solving... 相似文献
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Variational iteration method for solving time-fractional diffusion equations in porous the medium 下载免费PDF全文
<正>The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way.Some diffusion models with fractional derivatives are investigated analytically,and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order. 相似文献
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In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM soluti... 相似文献