耦合的凝聚态Bose-Einstein方程的双周期解

本文通过引入参数假设,利用雅可比椭圆函数展开法,得到了自散焦的耦合非线性Schr(o)dinger(NLS)方程的四种双周期解(雅可比椭圆函数).     

Universal Taylor Series on General Doubly Connected Domains

In this paper, a proof is given that there exists a universalTaylor series – in the sense of Nestoridis – inthe complement of a disk with respect to every center. Thisanswers a question asked by G. Costakis. 2000 Mathematics SubjectClassification 30B30.     

Remarks on Nonlinear Neumann Problems in Periodic Domains

We study a semilinear elliptic equation Au = f(x, u) with nonlinear Neumann boundary condition Bu = φ(ξ, u) in an unbounded domain Ω ? ?ⁿ, the boundary of which is defined by periodic functions. We assume that f and φ and the coefficients of the operators are asymptotically periodic in the space variables. Our main result states the existence of an asymptotically decaying, nontrivial solution of this problem with minimal energy. The proof is based on the concentration-compactness principle.     

Bingham Flows in Periodic Domains of Infinite Length

The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2? has a polynomial decay in ?, unlike in the Stokes case(see [Chipot,M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Math′ematiques Pures et Appliqu′ees, 90(2), 2008,133–159]) where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.     

分段双加权伪概周期函数及其分解唯一性

介绍了分段双加权伪概周期函数的概念.分段双加权伪概周期函数可以看做是分段加权伪概周期函数的推广也可以认为是双加权伪概周期函数的推广.首先给出分段双加权伪概周期函数的概念,然后介绍几个分段双加权伪概周期函数的几个性质:分解唯一性,分段双加权遍历空间的平移不变性.     

Symmetric Periodic Orbits and Uniruled Real Liouville Domains

A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.     

非线性电报方程组的3个双周期正解问题

主要考虑了带有双周期边值条件的耦合的非线性电报方程组的至少有3个双周期正解的存在性.首先利用线性电报方程的Green函数和极值原理,将非线性电报方程组解的存在性转化为算子的不动点.其次赋予非线性项一定的增长条件,然后利用有序Bamach空间锥上的Leggett-Williams不动点定理来证明算子在锥中至少存在3个不动点,即非线性电报方程组至少3个非负双周期解的存在性.     

Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching

Mathematical Notes - An asymptotic formula for the conformal module of a doubly connected domain symmetric about the abscissa axis under an unbounded stretching in the direction of this axis is...     

Approximation by Rational Functions on Doubly Connected Domains in Weighted Generalized Grand Smirnov Classes

Ukrainian Mathematical Journal - Let G ? ? be a doubly connected domain bounded by two rectifiable Carleson curves. We use the higher modulus of smoothness in order to investigate the...     

无界区域非自治随机sine-Gordon方程的D-周期吸引子

研究非自治随机sine-Gordon方程所生成的随机动力系统φ的D-周期吸引子的存在唯一性.运用一致估计得到了D的D-吸收集的存在性,并用分解技巧,证明了φ的渐近紧性,建立了动力系统φ在H~1(R~n)×L~2(R~n)中的D-周期吸引子的存在唯一性.当非自治外力项具有周期性时,该D-吸引子也呈现相同的周期性.     

带状区域中渐近周期曲率流方程的整体解

该文研究了具有渐近周期系数的曲率流方程的Neumann边值问题.首先,考虑一列初值问题及其相应的全局解,通过一致的先验估计取一个收敛子列,得到其极限就是一个整体解的结论.其次,向负无穷时间方向进行重整化,使用强极值原理证明了整体解的唯一性.最后,为了研究整体解的ω-和α-极限,再次使用重整化方法,通过构造拉回函数、进行...     

On Doubly Periodic Standing Wave Solutions of the Coupled Higgs Field Equation

In this paper, we derive a class of doubly periodic standing wave solutions for a coupled Higgs field equation by employing the Hirota bilinear method and theta function identities. Such solutions are expressed in terms of theta functions with variable separation form. Moreover, it is shown that these solutions can be converted into Jacobi elliptic function representations, and their long‐wave limit yields collision of dark solitons. In comparing with known solutions of the canonical evolution equation, three new aspects will be developed in this paper. First, the periods in the spatial and temporal directions, measured in terms of the theta function parameters τ and τ₁, are independent of each other, quite unlike most similar solutions found earlier in the literature. Second, the doubly periodic wave solutions possess two families of the local maxima, whose locations and types are then examined in detail. Third, we obtain new doubly periodic standing wave solutions for the Davey–Stewartson equation through its similarity transformation to the coupled Higgs field equation.     

Transport Properties of Doubly Periodic Arrays of Circular Cylinders and Optimal Design Problems

We solve an R -linear problem for a multiple-connected circular domain in a class of doubly periodic functions in analytic form by a method of functional equations. This problem models transport properties of two-dimensional composite materials made from a collection of disks embedded in an otherwise uniform host. Accepted 25 January 2001. Online publication 26 May 2001.     

双周期裂纹场平面弹性焊接的数学问题

本文讨论双周期胞腔中含任意形状裂纹的不同材料的弹性平面焊接(焊线为任意形状的封闭光滑曲线)的第二基本问题.运用Мусхелишвили复变函数方法,对这类弹性平面问题建立起了数学模型,将求解弹性平衡问题化归为寻求复应力函数满足一定边界条件的边值问题,然后构造其解的形式,再将其转化为正则型的奇异积分方程,数学上严格证明其解的存在与唯一.     

Periodic Gibbs Measures for the Ising Model with Competing Interactions

For the Ising model with competing interactions on the second-order Cayley tree, we find the operator corresponding to the periodic Gibbs distributions with period two and determine the invariant subsets of this operator, which are used to describe the periodic Gibbs distributions.     

An Estimate for the Attraction Domains of Difference Equations with Periodic Linear Terms

We consider the quasilinear systems of difference equations with periodic coefficients in linear terms. We obtain estimates for the attraction domain of the zero solution and establish inequalities for the norms of solutions. The results are stated in terms of Lyapunov-type matrix series.     

A Unified Integral Equation Scheme for Doubly Periodic Laplace and Stokes Boundary Value Problems in Two Dimensions

We present a spectrally accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. The basic idea is to use a small least squares solve to enforce periodic boundary conditions without ever handling periodic Green's functions. We describe fast solvers for the two‐dimensional (2D) doubly periodic conduction problem and Stokes nonslip fluid flow problem, where the unit cell contains many inclusions with smooth boundaries. Applications include computing the effective bulk properties of composite media (homogenization) and microfluidic chip design. We split the infinite sum over the lattice of images into a directly summed “near” part plus a small number of auxiliary sources that represent the (smooth) remaining “far” contribution. Applying physical boundary conditions on the unit cell walls gives an expanded linear system, which, after a rank‐1 or rank‐3 correction and a Schur complement, leaves a well‐conditioned square system that can be solved iteratively using fast multipole acceleration plus a low‐rank term. We are rather explicit about the consistency and nullspaces of both the continuous and discretized problems. The scheme is simple (no lattice sums, Ewald methods, or particle meshes are required), allows adaptivity, and is essentially dimension‐ and PDE‐independent, so it generalizes without fuss to 3D and to other elliptic problems. In order to handle close‐to‐touching geometries accurately we incorporate recently developed spectral quadratures. We include eight numerical examples and a software implementation. We validate against high‐accuracy results for the square array of discs in Laplace and Stokes cases (improving upon the latter), and show linear scaling for up to 10⁴ randomly located inclusions per unit cell. © 2018 Wiley Periodicals, Inc.