共查询到20条相似文献,搜索用时 140 毫秒
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为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解.
关键词:
sine-Gordon型方程
解的非线性叠加公式
辅助方程
无穷序列精确解 相似文献
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采用Darboux变换和一个积分变换,获得了两类双阱势Fokker-Planck方程准确解模型。严格解的结果同Kranmers近似作了比较。
关键词: 相似文献
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Runge-Kutta间断Galerkin法在求解Navier-Stokes方程中的应用 总被引:1,自引:0,他引:1
Cockburn & Shu[1] 在1988年提出了一种TVB Runge-Kuta局部投影的间断Galerkin有限元方法应用于Euler方程的求解,并取得了成功。文章将该方法进一步应用到Navier-Stokes方程的求解。 相似文献
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In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources. 相似文献
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Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method 下载免费PDF全文
D. B. Dhaigude & Gunvant A. Birajdar 《advances in applied mathematics and mechanics.》2014,6(1):107-119
In this paper we find the solution of linear as well as nonlinear
fractional partial differential equations using discrete Adomian
decomposition method. Here we develop the discrete Adomian decomposition
method to find the solution of fractional discrete diffusion equation,
nonlinear fractional discrete Schrodinger equation, fractional discrete
Ablowitz-Ladik equation and nonlinear fractional discrete Burger's equation.
The obtained solution is verified by comparison with exact solution when $\alpha=1$. 相似文献
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Zhen-Song Wang 《Letters in Mathematical Physics》1987,13(4):261-271
The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained. 相似文献
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M. N. Zhuravlev N. V. Ostrovskaya 《Journal of Experimental and Theoretical Physics》2004,99(2):427-442
The generalized moment method is applied to average the Ginzburg-Landau equation with quintic nonlinearity in the neighborhood of a soliton solution to the nonlinear Schrödinger equation. A qualitative analysis of the resulting dynamical system is presented. New soliton solutions bifurcating from a known exact soliton solution are obtained. The results of the qualitative analysis are compared with those obtained by direct numerical solution of the Ginzburg-Landau equation. 相似文献
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In this paper, to construct exact solution of nonlinear partial
differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By
the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived.
We investigate the short wave model for the Camassa-Holm equation
and the Degasperis-Procesi equation respectively. One-cusp soliton
solution of the Camassa-Holm equation is obtained. One-loop soliton solution of the Degasperis-Procesi equation is also obtained, the approximation of which in a closed form can be
obtained firstly by the Adomian decomposition method. The obtained
results in a parametric form coincide perfectly with those given
in the present reference. This illustrates the efficiency and
reliability of our approach. 相似文献
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Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients are studied using the solutions
of Raccati equation. The solitary wave-like solution, the trigonometric periodic wave solution and the rational wave solution
are obtained with a constraint between coefficients. The property of the solutions is numerically investigated. It is shown
that the coefficients of the equation do not change the wave amplitude, but may change the wave velocity.
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References: 《理论物理通讯》2007,47(2):333-338
For ion-acoustic waves in a plasma with non-isothermal electrons,the MKP equation is its governing equation.The instability of a soliton solution of MKP equation to two-dimensional long-wavelength perturbations is investigated up to the third order.It indicates that the one-soliton solution of MKP equation is unstable if v = -1wheras it is stable if v = 1 until the third order approximation has been considered. 相似文献