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61.
The Allen-Cahn equation ? Δu = u ? u 3 in ?2 has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u 3. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?3. 相似文献
62.
Jaume Llibre Marco Antonio Teixeira Joan Torregrosa 《Mathematical Physics, Analysis and Geometry》2007,10(3):237-249
The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum
periodic orbits of a k-dimensional isochronous center contained in ℝ
n
with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential
system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from
the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree.
As far as we know this is one of the first examples that this study can be made for a polynomial differential system having
a center and a non-rational first integral.
The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550.
The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the
joint project CAPES–MECD grant HBP2003-0017. 相似文献
63.
64.
《Particuology》2022
This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior. 相似文献
65.
《Wave Motion》2020
We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet–Bloch waves through an infinite array of scatterers. The approach lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics. 相似文献
66.
67.
本文用作者在文[1]引进的S 稳定的概念,给出了下面三个三阶非线性系统x~■+ax″+bx′+integral(t,x)=0;x~■+ax″+integral(t,x′)+cx=0;x~■+integral(t,x″)+bx′+cx=0存在唯一稳定周期解的充分条件,推广和改进了文[2—3]的工作. 相似文献
68.
多偏差变元中立型Rayleigh方程周期解问题 总被引:5,自引:0,他引:5
作者研究了一类多偏差变元中立型Rayleigh方程周期解问题,利用Mawhin重合度拓展定理得到了周期解存在性的新结果. 相似文献
69.
By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated. 相似文献
70.
A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model. 相似文献