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41.
A. N. W. Hone 《Transactions of the American Mathematical Society》2007,359(10):5019-5034
The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.
42.
具有转向点超曲面的奇摄动椭圆型方程边值问题 总被引:5,自引:0,他引:5
本文利用多重尺度法和比较定理,研究了n维空间中一类具有转向点超曲面的奇摄动椭圆方程边值问题,研究了该值问题解的渐近性态。 相似文献
43.
In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.
44.
Frank Natterer Olga Klyubina 《计算数学(英文版)》2007,25(3):368-373
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging. 相似文献
45.
46.
In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities. 相似文献
47.
Fritz Gesztesy Karl Unterkofler Rudi Weikard 《Transactions of the American Mathematical Society》2006,358(2):603-656
Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly describe the proper extension of the Airault-McKean-Moser locus associated with these three classes of algebro-geometric solutions of the KdV hierarchy with special emphasis on the case of multiple collisions between the poles of solutions. This solves a problem left open since the mid-1970s.
48.
A. Ducrot 《Mathematical Methods in the Applied Sciences》2007,30(3):291-304
This paper is devoted to the study of multi‐dimensional travelling wave solution for a thermo‐diffusive model, describing the propagation of curved flames in an infinite cylinder. The linear dependence of the components of the reaction rate together with the existence of an ignition temperature ensure that the corresponding linearized operator does not satisfy the Fredholm property. A direct consequence is that solvability conditions for the linearized operator are not known and classical methods of nonlinear analysis cannot be directly applied. We prove in this paper existence results of such travelling waves, by first introducing a suitable re‐formulation of the equations and then by choosing suitable weighted spaces that allows us to move the essential spectrum away from zero. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
49.
V. I. Inozemtsev 《Journal of statistical physics》1990,59(5-6):1143-1155
Extra integrals of motion and the Lax representation are found for interacting spin systems with the HamiltonianH = (J/2)
j, k=1,j k
N
P(j – k)
j
k
, where one of the periods of the WeierstrassP function is equal toN. The Heisenberg and Haldane-Shastry chains appear as limiting cases of these systems at some values of the second period. The simplest eigenvectors and eigenvalues ofH corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version. 相似文献
50.
P. N. Müller K. -D. Reinsch R. Bulirsch 《Journal of Optimization Theory and Applications》1994,80(2):367-372
In Ref. 1, the author claimed that the problem y=y
3 is soluble only for a certain range of the parameter . An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of . The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit 0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small is obtained using a three-variable approach. 相似文献