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1.
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u, ux)uxx +B(u, ux) is studied by using the conditional Lie–Ba¨cklund symmetry method. The variant forms of the considered equations,which admit the corresponding conditional Lie–Ba¨cklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. 相似文献
2.
It is shown that each one-parameter subgroup of SL(2,R) gives rise to a local correspondence theorem between suitably generic solutions of arbitrary scalar equations describing pseudo-spherical surfaces. Thus, if appropriate genericity conditions are satisfied, there exist local transformations between any two solutions of scalar equations arising as integrability conditions of sl(2,R)-valued linear problems.
A complete characterization of evolution equations ut=K(x,t,u,ux,…,uxk) which are of strictly pseudo-spherical type is also provided. 相似文献
3.
Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, uBB=uAB=−1, and for non-repulsive energy between AA nearest-neighbour sites, uAA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when uAA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of uAA. 相似文献
4.
研究一类具扰动的Sine-Gordon方程utt-uxx+αsinu-βuxxt=g(u),t>0,-∞< x< ∞的周期初值问题,提出了谱方法,并用先验估计方法作了误差估计,证明了近似方法的收敛性,并得到了该问题广义解的存在、唯一性。 相似文献
5.
On nonanalytic solitary waves formed by a nonlinear dispersion 总被引:7,自引:0,他引:7
Philip Rosenau 《Physics letters. A》1997,230(5-6):305-318
We study the prototypical, genuinely nonlinear, K(m, n) equation, ut ± a(um)x + (un)xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m, n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns. 相似文献
6.
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
7.
Helga Baum 《Journal of Geometry and Physics》1987,4(4):503-522
Let
(P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let DA be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote Tω:=
(DA(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (Tω · e-t(DA−f)2) near t=0 define 1-forms a(k)f, K=0, 1, 2, … on
(P). In this paper we calculate aa(0)f, a(1)f, a(2)f and study some of their properties. For instance using the 1-form a(2)f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S4. 相似文献
8.
H. Akbar-Zadeh 《Journal of Geometry and Physics》1995,17(4):342-380
A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F0(M, gt) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g0 F0(gt) of the integral I(gt) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (gt) for G = g0, then for a CID we show that for certain Finslerian manifolds, I″(g0) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs. 相似文献
9.
10.
考虑一类演化方程ut=au∂2k+1(其中a是常数,u∂2k+1=∂2k+1u/∂x2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。 相似文献
11.
We report new theoretical results and analysis for the transport properties of superconducting UPt3 based on the leading models for the pairing symmetry. We use Fermi surface data and the measured inelastic scattering rate to show that the low-temperature thermal conductivity and transverse sound attenuation in the A- and B-phase of UPt3 are in excellent agreement with pairing states belonging to the two-dimensional orbital E2u representation. 相似文献
12.
Partha Guha 《Journal of Geometry and Physics》2003,46(3-4):231-242
It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L2 metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S1. The space of differential operators Δ(n)=∂n+u2∂n−2++un form the space of extended or generalized projective connections. If a projective connection is factorizable Δ(n)=(∂−((n+1)/2−1)p1)(∂+(n−1)/2pn) with respect to quasi primary fields pi’s, then these fields satisfy ∑i=1n((n+1)/2−i)pi=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections. 相似文献
13.
Juan-Fang Han Dong-Ning Gao Heng Zhang Xiao-Yun Wang Wen-Shan Duan 《Frontiers of Physics》2015,10(5):105201
The effects of the dust size distribution in ultracold quantum dusty plasmas are investigated. The amplitude φm and width ω of quantum dust acoustic waves are studied with different dust size distributions in the system. The φm and ω of the quantum dust acoustic waves are found to increase as the total number density increases. The φm and ω are greater for unusual dusty plasmas than for typical dusty plasmas. Moreover, as the Fermi temperature of the dust grains increases, the φm of the wave decreases. The ω of quantum dust acoustic waves increases as the speed u0 of the wave increases. 相似文献
14.
色散方程的一类具任意稳定性的显格式 总被引:4,自引:0,他引:4
本文对色散方程ur=auxxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。 相似文献
15.
The global existence and structures of solutions to multi-dimensional unsteady compressible Euler equations are interesting
and important open problems. In this paper, we construct global classical solutions to the interaction of four orthogonal
planar rarefaction waves with two axes of symmetry for the Euler equations in two space dimensions, in the case where the
initial rarefaction waves are large. The bi-symmetric initial data is a basic type of four-wave two-dimensional Riemann problems.
The solutions in this case are continuous, bounded and self-similar, and we characterize how large the rarefaction waves must
be. We use the methods of hodograph transformation, characteristic decomposition, and phase space analysis. We resolve binary
interactions of simple waves in the process. 相似文献
16.
17.
P. Schobinger-Papamantellos K.H.J. Buschow 《Journal of magnetism and magnetic materials》1994,130(1-3):242-246
The magnetic ordering of the orthorhombic compound CeSi (Pama space group, FeB type of structure, Z = 4) Tn = 5.6 K was investigated by means of powder neutron diffraction in the temperatures 1.5 and 10 K. Our results show that the magnetic ordering is associated with a three dimensionally amplitude-modulated phase which is incommensurate with the crystal lattice with wave vector q = (qχ,qy,qz). The ordered Ce3+ moments are confined to the plane (a,b) at an angle of 16.7° with the b direction. It follows from the present data analysis that the dominant wave vector component is qz, which approximately corresponds to a transversal modulation, however the incommensurateness involves also the qx and qy components. The amplitude of the sine wave is μ0j = 1.667μB at 1.5 K which corresponds to quite a reduced ordered moment value compared to the Ce3+ free ion value gJ = 2.14μB. 相似文献
18.
The classical molecular dynamics simulations in canonical NVT ensemble conditions are used to investigate the melting transition in different heating rates of Pt-Ag-Au ternary nanoalloys. In order to obtain the initial configurations used in the molecular dynamics simulations, optimizing the chemical ordering of Pt13AgnAu42-n (n=0-42) ternary nanoalloys was performed using the Basin-Hopping algorithm which would not allow changes in the icosahedron structure. The Gupta many-body potential was used to model interatomic interactions in both molecular dynamics simulations and optimization simulations. The melting transitions of selected Pt-Ag-Au nanoalloys were explored using caloric curves and Lindemann parameters. There have been two identified types of melting mechanisms, one includes sudden jump behavior in the caloric curve and the other is an isomerization while melting transition. The temperature range in which the isomerization takes place depends on the heating rate value. 相似文献
19.
Electrooptical Kerr effect has been studied in binary solutions of a dipolar liquid (-picoline, β-picoline) in a non-dipolar solvent (benzene, p-xylene) and 1,4-dioxane in the full range of concentrations of the dipolar component (0 ≤ f2 ≤ 1). The experimental Kerr constant Ks of the solutions, refraction index ns, density ρs and the dielectric constant εs have been measured and used for the calculation of the molar Kerr constants KSM within the Onsager local field model. Analysis of changes in the molar Kerr constants as a function of the solute concentration by fits of theoretical functions to the experimental ones has permitted a determination of the parameters characterizing intermolecular interactions in binary solutions. 相似文献
20.
We study the Cauchy problem for the Whitham modulation equations for increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, ... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so-called hodograph transformation introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each g>0, we construct the unique solution of the Tsarev system, which matches the genus g+1 and g–1 solutions on the transition boundaries. 相似文献