Fisher方程的有界衰减振荡解

为了研究非线性发展方程的有界衰减振荡解,特选取Fisher方程为例. Fisher方程在描述激发介质的非数值模型(如Belousov-Zhabotinsky (BZ)反应)中, 其解的振幅取负值是有意义的.应用平面动力系统理论,研究了Fisher方程有界行波解存在的条件, 利用LS解法和线性化解法给出了其有界衰减振荡解的近似解析表达式,并进行了误差估计.     

Memory effects in Fisher equation with nonlinear convection term

Memory effect in diffusion–reaction equation plays important role in physical, biological and chemical sciences. An exact solutions of Fisher equation in the presence of nonlinear convection term with finite memory transport is obtained. Solutions of corresponding diffusion–reaction equation without memory effect is also obtained and a comparison is made between obtained solutions. In particular, the solitary wave solutions are found.     

变系数KP方程新的类孤波解和解析解

用普通Sine-Gordon的行波变换方程，提出了一种新的求解变系数Kaolomtsev-Petviashvili(KP)方程的方法，获得了变系数KP方程新的类孤波解、类Jacobi椭圆函数解和三角函数解. 关键词： 变系数KP方程 Sine-Gordon方程 类椭圆函数解 类孤波解     

The Fokker-Planck equation in the second-order pitch angle approximation and its exact solution

The diffusive particle propagation and its pitch angle scattering is studied using kinetic equation of the Fokker-Planck form. The case is considered when charged particles preferable propagate along the strong mean magnetic field direction and undergo the pitch angle scattering with respect to it. The paper deals with solution of the equation for particle distribution function in the second-order approximation in the pitch angle. The exact analytical solution is obtained in an integral form. The well-known solution in the first-order pitch angle approximation can be restored performing the small time limit in the result. Unlike the first-order solution the obtained solution in the second approximation rightly shows that the pitch angle diffusion is closely connected with the particle transport along the mean magnetic field. The expression for particle density for the point instantaneous unidirectional source also has been obtained.     

LS解法和Fisher方程行波系统的定性分析

提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统.     

Anomalous biennial oscillations in a Fisher equation with a discretized verhulst term

The dynamics of a biological population governed by a modified Fisher equation is studied by means of Monte Carlo simulations. Reproduction of the population occurs at discrete times, while transport caused by diffusion and conduction takes place on shorter time scales. The discrete reproduction, modeled with a set of coupled logistic maps, exhibits phenomena which are not evident in the usual continuum version of the Fisher equation. Several mechanisms for biennial oscillations of the total population are investigated. One of these shows an ordered coupling between random diffusive motion and the chaotic attractor of the logistic map.     

An exact solution of Laplace's equation for cuspidal geometry

An exact solution of Laplace's equation is obtained for a system of conducting electrodes with cuspidal symmetry. The significance of this result in predicting and verifying the equilibrium configuration of a rotationally symmetric conducting fluid subject to electrostatic stress is discussed.This work was supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-8108829     

An exact solution to the multi-dimensional line transfer equation

The theory of generalized analytic functions is used to obtain an exact closed form analytical solution to a transfer problem for spectral line radiation in a multi-dimensional atmosphere. The multi-dimensional full-space and half-space Green's functions so obtained are quite general and may be used, along with the corresponding orthogonality relationships, to obtain solutions to any general multi-dimensional radiative transfer problem involving model two-level atoms. An application of the method using perturbation techniques is illustrated.     

An exact solution of Einstein's equation with a dilaton field

An exact solution of Einstein gravity coupled to a dilaton field is found. The solution is conformally flat and is invariant under Lorentz transformations. The singularities and conformal structure of the metric are examined.     

An exact solution of the Korteweg-de Vries equation with dissipation

By means of the method proposed in the papers [1, 2] we look for solutions of the Korteweg—de Vries equation with dissipation. A new solution is found and expressed by means of the Weierstrass P-function.Partially supported by NSF Grant No. INT 73.20002 A01 formerly GF-41958.     

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     

An exact solution for the linearized multifrequency radiation diffusion equation

An exact solution, based on Fourier and Laplace (FL) transforms, is developed for a linearization of the system modeling the multifrequency radiation diffusion and matter energy balance equations. The model uses an ideal gas equation of state. Opacities are proportional to the inverse of the cube of the frequency, thereby simulating free-free transitions. The solution is obtained in terms of integrals over the FL coefficients of the initial conditions and explicit sources. Results are presented for two special cases. (1) No sources, initially cold radiation field, and a localized matter energy profile. (2) Initially cold matter and radiation fields and a source of matter energy extending over finite space and time intervals.     

Subjective modelling of supply and demand—the minimum of Fisher information solution

Two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand/supply profiles if one considers closing of a position as a random process. We would like to present the analysis of a subjectivity in such trading models. In our model, the trader gets the maximal profit intensity when the probability of transaction is ∼0.5853. We also present a comparison with the model based on the Maximum of Entropy Principle. To the best of our knowledge, this is one of the first analyses that show a concrete situation in which trader profit optimal value is in the class of price-negotiating algorithms (strategies) resulting in non-monotonic demand (supply) curves of the Rest of the World (a collective opponent). Our model suggests that there might be a new class of rational trader strategies that (almost) neglects the supply-demand profile of the market. This class emerges when one tries to minimize the information that strategies reveal.     

Quantum Fisher Information and Uncertainty Relations

It is well known that the Cramér–Rao inequality places a lower bound for quantum Fisher information in terms of the variance of any quantum measurement. We establish an upper bound for quantum Fisher information of a parameterized family of density operators in terms of the variance of the generator. These two bounds together yield a generalization of the Heisenberg uncertainty relations from statistical estimation perspective.     

Hirota方程的怪波解及其传输特性研究

求出了高阶Hirota方程在可积条件下的一种精确呼吸子解,并基于此呼吸子解得到了Hirota方程的一种怪波解.在此怪波解的基础上研究了怪波的激发,发现对平面波进行周期性扰动可以激发怪波,对平面波进行高斯扰动可以更快地激发怪波,还可以直接在常数项上增加高斯扰动激发怪波.作为一个实例,采用分步傅里叶方法数值研究了在考虑自频移和拉曼增益时怪波的传输特性,自频移使怪波中心发生偏移,拉曼增益使得怪波分裂得更快,而且拉曼增益值越大怪波分裂得越快,但是拉曼增益对怪波的峰值强度没有明显影响.最后数值模拟了相邻怪波之间的相互作用特点,随着怪波之间距离的减小,怪波将合二为一,成为一束怪波,之后再分裂,并分析了拉曼增益和自频移对怪波相互作用的影响.     

A new exact solution and corresponding localized excitations of the ()-dimensional mKdV equation

In this Letter, we show that the new (2+1)-dimensional mKdV equation possesses Painlevé property. Then, starting from the standard truncated Laurent expansion and the direct variable separation approach, a new exact solution with two lower dimensional arbitrary functions is obtained. Some high-dimensional localized excitations of the physical quantity u are constructed. These localized excitations have abundant structures at x-axis and y-axis such as dromions, peakons, loop-solitons, compactons which depend on corresponding functions.     

New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation

In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov--Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.     

Volterra差分微分方程和KdV差分微分方程新的精确解

辅助方程法和试探函数法为基础,给出函数变换与辅助方程相结合的一种方法,借助符号计算系统Mathematica构造了Volterra差分微分方程和KdV差分微分方程新的精确孤立波解和三角函数解.该方法也适合求解其他非线性差分微分方程的精确解. 关键词： 辅助方程 函数变换 非线性差分微分方程 孤立波解     

The exact solution and integrable properties to the variable-coefficient modified Korteweg-de Vries equation

In this paper, a variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation is investigated. With the help of symbolic computation, the N-soliton solution is derived through the Hirota method. Then the bilinear Bäcklund transformations and Lax pairs are presented. At last, we show some interactions of solitary waves.