共查询到19条相似文献,搜索用时 78 毫秒
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本文研究n体聚集过程和联合聚集过程的集团分布演化。从广义Smoluchovki方程出发,给出聚集核K(i1,i2,…,in)=A sumfrom i=1 to n i1+B(A,B均为常数)的显解;利用聚集核K(i1,i2,…,in)=(Ai1+B)(Ai2+B)…(Ain+B)和核K(i1,i2,…,in)=A sumfrom i=1 to n i1+B的方程之间的联系,得出核K(i1,i2,…,in)=S(i1)S(i2)…S(in)(SK=AK+B)的凝前解。而且,根据联合聚集动力学方程,讨论了聚集和型核分别为K2(i,j)=i+j,K3(i,j,k)=i+j+k的集团尺寸分布Cm(t)的长时行为,并将结论推广到一般的联合聚集过程。
关键词: 相似文献
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本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)ut=(g(x)D(u)ux)x+h(x)P(u)ux+q(x)Q(u)进行研究. 当扩散项D(u)取um (m≠-1,0,1)和eu两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解.
关键词:
广义条件对称
精确解
非线性反应扩散方程 相似文献
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利用半度规λ(α)μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω(α)μ≡-cλ(α)μ,给出一个具有广义协变的包含重力场贡献的重力场方程Rμν-gμνR/2+Λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν)
关键词:
重力场方程
协变形式
能量-动量张量
量子化 相似文献
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本文研究了推广的KdV方程 ut+2μuux+v3x+δu5x=0(μvδ≠0) (1)的精确孤子解,得到了(1)式的一些新的孤波解,对文献[10]的若干结论作了补充与修正。
关键词: 相似文献
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文章用提拉法生长出Li6Gd(BO3)3:Ce晶体,并对其光谱性能与发光过程进行了探索. 借助于真空紫外-紫外透过光谱测试,发现晶体的透过光谱中存在Ce3+离子和Gd3+的特征吸收峰,同时还存在与Ce4+离子相关的电荷迁移带. 对晶体的真空紫外-紫外激发发射光谱进行研究发现,在晶体存在着Ce3+离子的5d→4f辐射跃迁发光与Gd3+离子的4f→4f辐射跃迁发光,而且存在着Gd3+→Ce3+之间的能量传递. 对Li6Gd(BO3)3:Ce晶体的X射线与γ射线激发发射光谱研究可知,晶体在高能射线激发下的闪烁光主要是Ce3+离子的发光.
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6Gd(BO3)3:Ce晶体')" href="#">Li6Gd(BO3)3:Ce晶体
真空紫外-紫外透过光谱
真空紫外-紫外激发发射光谱
能量传递 相似文献
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The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and some of which are derived for the first time. It is concluded from the results that this approach is simple and efficient even in solving partial differential equations with variable coefficients. 相似文献
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In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 + BF2+p + CF2+2p (where F1= dF/dε, p 〉 0) are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 (2007) 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 (2008) 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics. 相似文献
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On the Riemann–Hilbert problem of a generalized derivative nonlinear Schrödinger equation 总被引:1,自引:0,他引:1
In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schr?dinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line. 相似文献
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The conservation laws for the (1+2)-dimensional Zakharov-Kuznetsov modified equal width (ZK-MEW) equation with power law nonlinearity are constructed by using Noether's approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation. 相似文献
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HUANG Ye-Hui WU Hong-Xia XIE Xi ZENG Yun-Bo 《理论物理通讯》2008,49(5):1091-1100
The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS. 相似文献
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JIA Yi-Feng CHEN Yu-Fu 《理论物理通讯》2008,49(5):1139-1144
In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given. 相似文献
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The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equation are explored by the method of the improved generalized auxiliary differential equation. Many explicit analytic solutions of the Z-K equation are obtained. The methods used to solve the Z-K equation can be employed in further work to establish new solutions for other nonlinear partial differential equations. 相似文献