Approximation of the soliton solution for the generalized Vakhnenko equation

A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.     

广义Landau-Ginzburg-Higgs方程孤子解的扰动理论

利用扰动方法研究了一类广义Landau-Ginzburg-Higgs方程.引入一个同伦映射，将原方程的解表示为渐近展开式，然后用相应的线性方程的解来近似地表示.讨论了方程的解与得到的近似解的关系. 关键词： 孤子 扰动 同伦映射     

A perturbation solution to generalized linear Boltzmann equation

A perturbation method to solve the generalized linear Boltzmann equation is presented for the calculation of dynamic conductivity of a normal metal at low temperatures. The method is applied to the ordinary Boltzmann equation. The following three cases are considered: i) when only electron-impurity interactions are dominant, ii) when the metal may be considered as pure plasma, and iii) when both of the interactions are present. The expressions for conductivity are presented in the binary collision approximation. The connected diagram expansion method is extended for the direct calculation of the conductivity. Finally the method is extended for the calculation of conductivity by the correlation function formula.     

(2+1)-维Wick类型随机广义KP方程的类孤子解

利用埃尔米特变换和特殊的截断展开法求出(2+1)-维Wick类型随机广义KP方程的类孤子解. 这种方法的基本思想是通过埃尔米特变换把(2+1)-维Wick类型随机广义KP方程变成的(2+1)-维广义变系数KP方程,利用特殊的截断展开方法求出方程的解,然后通过埃尔米特的逆变换求出方程的随机解.     

A periodic solution of the Lorenz equation in the high Rayleigh number limit

A periodic solution, which the Lorenz equation has in the limit of high Rayleigh number r, is calculated up to the first order in $\text{?=}\text{1}\text{(r?1)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ by using the perturbation theory of nonlinear oscillations.     

广义Boussinesq方程的同伦映射近似解

研究了一个广义非线性Boussinesq方程. 利用同伦映射方法,首先构造了相应的同伦变换;其次选取了适当的初始近似;然后用同伦映射方法得到了孤立子波近似解;最后得到了微扰渐近表示式. 关键词： Boussinesq方程 非线性 孤立子 近似方法     

一类广义Sine-Gordon扰动方程的解析解

利用同伦映射方法研究了一类广义Sine-Gordon方程. 首先引入一个同伦变换. 然后构造了原方程解的迭代关系式. 最后得到了问题的解析解. 关键词： 孤子 扰动 同伦映射     

广义非对称Hartmann势Klein-Gordon方程的严格解(英文)

在标量势和矢量势相等的条件下,严格求解了在广义非对称Hartmann势场中粒子运动的Klein Gordon方程;并利用束缚态边界条件,获得了束缚态能谱表达式和由超几何函数表示出的波函数.     

1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation

This Letter carries out the integration of the generalized Radhakrishnan, Kundu, Lakshmanan equation to obtain the 1-soliton solution. The solitary wave ansatz is used to carry out the integration, to obtain an exact solution of this equation.     

广义随机KdV方程新的精确类孤子解

利用厄米(Hermite)变换求出了广义随机KdV方程新的类孤子解.这种方法的基本思想是通过厄米变换把Wick类型的广义随机KdV变成广义变系数KdV方程，利用特殊的截断展开方法求出 方程的解，然后通过厄米的逆变换求出方程的随机解. 关键词： 随机KdV方程 随机孤子解 白色噪音 截断展开方法 厄米变换     

On the equivalence of generalized Langevin equation and generalized master equation

It is shown that the generalized Langevin equation derived by Mori is equivalent to the generalized master equation of Nakajima and Zwanzig. Both equations of motion are related, just in the same way as Heisenberg and Schrödinger picture are related.     

A direct solution of the radiative transfer equation: Application to Rayleigh and Mie atmospheres

A direct method is given for the solution of the spherical harmonics approximation to the equation of radiative transfer in plane-parallel atmospheres. Although the method is formulated theoretically for non-homogeneous atmospheres with an arbitrary phase function, at present it has only been implemented for homogeneous atmospheres. Test computations performed for Rayleigh and Mie scattering phase functions show that the direct method is unconditionally stable and solves efficiently problems both for optically thin and very thick atmospheres. Timing comparisons with the method of Chandrasekhar for Rayleigh atmospheres and with an integral-equation iterative method for Mie atmospheres are quite favorable to the proposed method.     

Analytical solution of the generalized smoluchowski problem using a new model kinetic equation

A new kinetic equation whose solution yields a correct Prandtl number is suggested. A technique for analytically solving half-space boundary-value problems is demonstrated with the classical Smoluchowski problem of finding temperature and concentration steps. Numerical results indicating the succession of the equation.     

非线性广义Landau-Ginzburg-Higgs方程孤子解的变分迭代解法

利用扰动方法研究了一类非线性广义Landau-Ginzburg-Higgs方程.首先引入一个泛函，计算它的变分，求得Lagrange乘子.然后构造了原方程解的迭代关系式，得到了近似解. 关键词： 孤子 扰动 变分迭代     

Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method

The generalized projective Riccati equation method is proposed to establish exact solutions for generalized form of the reaction Duffing model in fractional sense namely, Khalil’s derivative. The compatible traveling wave transform converts the governing equation to a non linear ODE. The predicted solution is a series of two new variables that solve a particular ODE system. Coefficients of terms in the series are calculated by solving an algebraic system that comes into existence by substitution of the predicted solution into the ODE which is the result of the wave transformation of the governing equation. Returning original variables give exact solutions to the governing equation in various forms.     

Periodic solutions of the Ginzburg-Landau equation

Spatially periodic solutions to the Ginzburg-Landau equation are considered. In particular we obtain: criteria for primary and secondary bifurcation; limit cycle solutions; nonlinear dispersion relations relating spatial and temporal frequencies. Only relatively simple tools appear in the treatment and as a result a wide range of parameter cases are considered. Finally we briefly treat the case of spatial bifurcations.     

1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.     

Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of O(k2+ h2).Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.     

The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation

This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping, it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method, it possesses a good accuracy.