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91.
为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解.
关键词:
sine-Gordon型方程
解的非线性叠加公式
辅助方程
无穷序列精确解 相似文献
92.
首次提出产生局域空心光束(Bottle beam)的另一类新型锥透镜模型.讨论了凹凸两种模型,分别是在传统轴棱锥的底部磨削和胶合圆台结构形成.研究结果表明平面波正入射新型凹锥透镜可产生单个Bottle beam,正入射新型凸锥透镜可形成具有周期性的Bottle beam.通过几何光学分析了产生Bottle beam的原理,计算了Bottle beam的相关参数.由衍射积分理论分析和模拟了新型锥透镜后的光强分布特性,所得分析结果与几何光学分析基本符合.
关键词:
新型锥透镜
Bottle beam
轴棱锥
Bessel光 相似文献
93.
Noritaka Iwai 《Journal of fluorine chemistry》2009,130(4):434-6943
Isolation of bacterial strains capable of degrading fluorinated materials was described. 8 strains of Actinobacteria exhibited degradability of ethyl difluoroacetate (DFAc) was accumulated by bacteria, giving difluoroacetic acid and then fluoride ion. Further, 13 strains of Actinobacteria exhibited degradability of fluorobenzene and/or benzotrifluoride. In batch culture, growth of strains on fluorinated materials led to the release of fluoride ion. 相似文献
94.
M.J. Grannell 《Discrete Mathematics》2009,309(9):2847-2860
We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n+1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n+7. 相似文献
95.
96.
Wiesaw Kubi 《Journal of Mathematical Analysis and Applications》2009,350(2):758-257
A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to Σ-spaces. We characterize the existence of a projectional skeleton in terms of elementary substructures, providing simple proofs of known results concerning weakly compactly generated spaces and Plichko spaces. We prove a preservation result for Plichko Banach spaces, involving transfinite sequences of projections. As a corollary, we show that a Banach space is Plichko if and only if it has a commutative projectional skeleton. 相似文献
97.
Anthony Flatters 《Journal of Number Theory》2009,129(1):209-219
We study primitive prime divisors of the terms of Δ(u)=(Δn(u))n?1, where Δn(u)=NK/Q(un−1) for K a real quadratic field, and u a unit element of its ring of integers. The methods used allow us to find the terms of the sequence that do not have a primitive prime divisor. 相似文献
98.
The structured Bessel-type functions of arbitrary even-order were introduced by Everitt and Markett in 1994; these functions satisfy linear ordinary differential equations of the same even-order. The differential equations have analytic coefficients and are defined on the whole complex plane with a regular singularity at the origin and an irregular singularity at the point of infinity. They are all natural extensions of the classical second-order Bessel differential equation. Further these differential equations have real-valued coefficients on the positive real half-line of the plane, and can be written in Lagrange symmetric (formally self-adjoint) form. In the fourth-order case, the Lagrange symmetric differential expression generates self-adjoint unbounded operators in certain Hilbert function spaces. These results are recorded in many of the papers here given as references. It is shown in the original paper of 1994 that in this fourth-order case one solution exists which can be represented in terms of the classical Bessel functions of order 0 and 1. The existence of this solution, further aided by computer programs in Maple, led to the existence of a linearly independent basis of solutions of the differential equation. In this paper a new proof of the existence of this solution base is given, on using the advanced theory of special functions in the complex plane. The methods lead to the development of analytical properties of these solutions, in particular the series expansions of all solutions at the regular singularity at the origin of the complex plane. 相似文献
99.
This paper considers a homotopy perturbation method for approximating multivariate vector-value highly oscillatory integrals. The asymptotic formulae of the integrals and the asymptotic order of the asymptotic method are presented. Numerical examples show the efficiency of the approximation method. 相似文献
100.
Ioannis K. Argyros 《Applied mathematics and computation》2009,215(4):1553-1560
We provide sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear operator equation containing operators that are Fréchet-differentiable of order at least two, in a Banach space setting. Numerical examples are also provided to show that our results apply to solve nonlinear equations in cases earlier ones cannot [J.M. Gutiérrez, A new semilocal convergence theorem for Newton’s method, J. Comput. Appl. Math. 79(1997) 131-145; Z. Huang, A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211-217; F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Mathematica 5 (1985) 71-84]. 相似文献