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 共查询到17条相似文献,搜索用时 93 毫秒
1.
利用同伦分析法求解了Burgers方程,得到了其扭结形孤立波的近似解析解,该解非常接近于相应的精确解.结果表明,同伦分析法可用来求解非线性演化方程的孤立波解.同时,也对所用方法进行了一定扩展,得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词: Burgers方程 同伦分析法 KP方程 孤立波解  相似文献   

2.
石玉仁  汪映海  杨红娟  段文山 《物理学报》2007,56(12):6791-6796
利用同伦分析法求解了修正的Kadomtsev-Petviashvili方程, 得到了它的近似孤立波解, 该解与精确解符合得非常好.结果表明,同伦分析法在求解高维非线性演化方程的孤立波解时, 仍然是一种行之有效的方法. 关键词: 同伦分析法 修正的Kadomtsev-Petviashvili方程 孤立波解  相似文献   

3.
杨沛  陈勇  李志斌 《物理学报》2010,59(6):3668-3673
将同伦分析法进行了推广,使之适用于求解离散修正KdV方程.获得了由指数函数表达的亮孤子解,该解析近似解与精确解符合很好.数值模拟结果说明了同伦分析法对求解复杂非线性问题的有效性和潜力.  相似文献   

4.
利用同伦分析法求解了KdV-Burgers方程,得到了它的解析近似解,该解与精确解符合得非常好.结果表明同伦分析法在求解某些耗散系统时,仍然是一种行之有效的方法.  相似文献   

5.
莫嘉琪  程荣军  葛红霞 《物理学报》2011,60(4):40203-040203
研究了一类具有非线性阻尼力和强迫周期力项的相对转动非线性动力学模型. 首先构造一个同伦映射, 其次决定方程的初始近似, 最后通过同伦映射方法得到了对应模型的任意次近似解. 关键词: 相对转动 非线性动力系统 近似解  相似文献   

6.
尹君毅 《物理学报》2014,63(23):230202-230202
对(G′/G)展开法做了进一步的研究,利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题.借助Riccati方程的B?cklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解.这样,利用(G′/G)展开法可以获得非线性发展方程的无穷序列解,这一方法是对已有方法的扩展,与已有方法相比可获得更丰富的无穷序列解.以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解.这一方法可以用来构造其他非线性发展方程的无穷序列解.  相似文献   

7.
石兰芳  莫嘉琪 《物理学报》2009,58(12):8123-8126
采用一个简单而有效的技巧,研究了一类扰动非线性发展方程.首先,引入一个相应典型方程的孤子近似解.然后,利用同伦映射方法得到了原扰动非线性发展方程的近似解. 关键词: 孤子 扰动发展方程 同伦映射  相似文献   

8.
微重力下圆管毛细流动解析近似解研究   总被引:2,自引:0,他引:2       下载免费PDF全文
李永强*  张晨辉  刘玲  段俐  康琦 《物理学报》2013,62(4):44701-044701
应用同伦分析法研究微重力环境下圆管毛细流动解析近似解问题, 给出了级数解的表达公式. 不同于其他解析近似方法, 该方法从根本上克服了摄动理论对小参数的过分依赖, 其有效性与所研究的非线性问题是否含有小参数无关, 适用范围广. 同伦分析法提供了选取基函数的自由, 可以选取较好的基函数, 更有效地逼近问题的解, 通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度, 同伦分析法为圆管毛细流动问题的解析近似求解开辟了一个全新的途径. 通过具体算例, 将同伦分析法与四阶龙格库塔方法数值解做了比较, 结果表明, 该方法具有很高的计算精度. 关键词: 圆管 微重力 毛细流动 同伦分析法  相似文献   

9.
李永强  刘玲  张晨辉  段俐  康琦 《物理学报》2013,62(2):24701-024701
应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度.  相似文献   

10.
吴钦宽 《物理学报》2008,57(5):2654-2657
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   

11.
We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter h, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.  相似文献   

12.
The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik–Novikov–Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using \(G'/G\) expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using \(G'/G\) expansion method are compared with the approximate analytical solutions attained by employing HAM.  相似文献   

13.
This Letter deals with compact and noncompact solutions for nonlinear evolution equations with time-fractional derivatives. We present a reliable approach of the homotopy perturbation method to handle nonlinear fractional evolution equations. The validity of the approach is verified through illustrative examples. New exact solitary wave and compacton solutions are developed. The proposed technique could lead to a promising approach for a wide class of nonlinear fractional evolution equations.  相似文献   

14.
李德生  张鸿庆 《物理学报》2004,53(6):1639-1642
从B-cklund变换出发,利用Cole-Hopf变换,一些有重要物理意义的(2+1)维非线性演化方程(组)被简化为具有两个分别关于(x,t),(y,t)的任意函数的单个线性偏微分方程.通过对该方程解的研究,获得了原方程一些新的精确解.其中,一些近年来被广泛研究的由分离变量法所获得的解也被重新得到. 关键词: B-cklund变换 Cole-Hopf变换 分离变量法 精确解  相似文献   

15.
The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].   相似文献   

16.
We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions.  相似文献   

17.
Nonlinear Evolution Equations with Gradient Coupled Noise   总被引:1,自引:0,他引:1  
We show existence and uniqueness of solutions for a class of nonlinear evolution equations with gradient coupled noise. Our results are obtained by using a simple transformation relating the equation under consideration to an underlying deterministic partial differential equation. Both the Itô and the Stratonovich conventions are treated. Several examples show that the properties of solutions for Itô equations can differ significantly from those of Stratonovich equations.  相似文献   

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