Decay and stability of solutions to the Fokker–Planck–Boltzmann equation in

In this paper, we use the method of constructing the compensating function introduced by Kawashima and the standard energy method to study the global existence of solutions to the Fokker–Planck–Boltzmann equation in the whole space. The time decay and uniform stability of solutions to the global Maxwellian are also obtained.     

Optimal convergence rate of the landau equation with frictional force

The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.     

Ginzburg-Landau方程动力性态的Fourier谱逼近

0　引言和符号立方Schrodinger方程或更一般的形式Ginzburg-Landau方程出现在许多物理和化学问题中.例如在非线性光学的细束流中有方程2ikux+2⊥u+n2n0k2|u|2u=0对于二维流,有方程n2n0k2|u|2u=-2kiut-uxx-uyy还有等离子体的Langmuir波;一维单色波的自调制;二维定态平面波的自聚集;在非相对论下超导电子对在电磁场中运动等均可用非线性Schrodinger方程和Ginzburg-Landau方程来描述[1-4].另外,反应扩散方程描述的化学反应方程的研究中也出现Ginzburg-Landau方程,如相对于稳态浓度c*的扰动浓度c-c*就满足Ginzburg-Landau方程[5,6].由…     

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.     

Stable transmission of solitons in the complex cubic–quintic Ginzburg–Landau equation with nonlinear gain and higher-order effects

In this paper, a complex cubic–quintic Ginzburg–Landau equation (CCQGLE) is investigated. Using the asymmetric method, the analytic one-soliton solution of the CCQGLE is obtained for the first time. Through analyzing the solutions obtained, the transmission of the soliton is controlled by changing the values of related parameters. Results of this paper contribute to obtain the analytic soliton solution of the higher-order CCQGLE.     

Fractional traveling wave solutions of the (2 + 1)-dimensional fractional complex Ginzburg–Landau equation via two methods

A (2 + 1)-dimensional fractional complex Ginzburg–Landau equation is solved via fractional Riccati method and fractional bifunction method, and exact traveling wave solutions including soliton solution and combined soliton solutions are constructed based on Mittag–Leffler function. A series of fractional orders is used to demonstrate the graphical representation and physical interpretation of the resulting solutions. The role of the fractional order is revealed.     

三维广义磁流体方程组解的最优衰减率

本文利用Fourier分解法首次建立了三维广义磁流体动力学方程组弱解的时间衰减估计,得到了该方程解关于时间衰减的上下界估计,并且获得了相应的最优代数衰减率.     

Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

We present a class of orthogonal functions on infinite domain based on Jacobi polynomials. These functions are generated by applying a tanh transformation to Jacobi polynomials. We construct interpolation and projection error estimates using weighted pseudo-derivatives tailored to the involved mapping. Then, using the nodes of the newly introduced tanh Jacobi functions, we develop an efficient spectral tanh Jacobi collocation method for the numerical simulation of nonlinear Schrödinger equations on the infinite domain without using artificial boundary conditions. The applicability and accuracy of the solution method are demonstrated by two numerical examples for solving the nonlinear Schrödinger equation and the nonlinear Ginzburg–Landau equation.     

A Finite-difference Solution of the Ginzburg–Landau Equation

Two finite-difference methods, which differ only in the way that they approximate the derivative boundary conditions, are developed for solving a particular form of the complex Ginzburg–Landau equation of superconductivity. The non-linear term in this equation is linearized in a way familiar to readers of Professor Mickens' work, and the numerical solution is obtained at each time step by solving a linear algebraic system. Consistency and stability are discussed and some numerical results are reported.     

A REGULARIZATION NEWTON METHOD FOR MIXED COMPLEMENTARITY PROBLEMS

In this paper, a regularization Newton method for mixed complementarity problem(MCP) based on the reformulation of MCP in [1] is proposed. Its global conver-gence is proved under the assumption that F is a Po-function. The main feature of our algorithm is that a priori of the existence of an accumulation point for convergence need not to be assumed.     

Acoustic limit for the Boltzmann equation in the whole space

This paper is devoted to the following rescaled Boltzmann equation in the acoustic time scaling in the whole space

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