共查询到20条相似文献,搜索用时 15 毫秒
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María Elena Luna‐Elizarrarás Marco Antonio Pérez‐de la Rosa Ramón M. Rodríguez‐Dagnino Michael Shapiro 《Mathematical Methods in the Applied Sciences》2013,36(9):1080-1094
It has been found recently that there exists a theory of functions with quaternionic values and in two real variables, which is determined by a Cauchy–Riemann‐type operator with quaternionic variable coefficients, and that is intimately related to the so‐called Mathieu equations. In this work, it is all explained as well as some basic facts of the arising quaternionic function theory. We establish analogues of the basic integral formulas of complex analysis such as Borel–Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. This theory turns out to be in the same relation with the Schrödinger operator with special potential as the usual holomorphic functions in one complex variable, or quaternionic hyperholomorphic functions, or functions of Clifford analysis, are with the corresponding Laplace operator. Moreover, it is similar to that of α‐hyperholomorphic functions and the Helmholtz operator. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Seak‐Weng Vong Qing‐Jiang Meng Siu‐Long Lei 《Numerical Methods for Partial Differential Equations》2013,29(2):693-705
We consider a discrete‐time orthogonal spline collocation scheme for solving Schrödinger equation with wave operator. The scheme is proposed recently by Wang et al. (J Comput Appl Math 235 (2011), 1993–2005) and is showed to have high‐order convergence rate when a parameter θ in the scheme is not less than $\frac{1}{4}$. In this article, we show that the result can be extended to include $\theta\in(0,\frac{1}{4})$ under an assumption. Numerical example is given to justify the theoretical result. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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Laurent Bakri Jean‐Baptiste Casteras 《Mathematical Methods in the Applied Sciences》2014,37(13):1992-2008
We give a sharp upper bound on the vanishing order of solutions to the Schrödinger equation with electric and magnetic potentials on a compact smooth manifold. Our main result is that the vanishing order of nontrivial solutions to Δu + V · ? u + Wu = 0 is everywhere less than . Our method is based on quantitative Carleman type inequalities, and it allows us to show the following uniform doubling inequality which implies the desired result. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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In this paper we study the regularity theory for the Schrödinger equations under proper conditions. Furthermore, it will be verified that these conditions are optimal. 相似文献
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In this article we will study the initial value problem for some Schrödinger equations with Dirac-like initial data and therefore with infinite L2 mass, obtaining positive results for subcritical nonlinearities. In the critical case and in one dimension we prove that after some renormalization the corresponding solution has finite energy. This allows us to conclude a stability result in the defocusing setting. These problems are related to the existence of a singular dynamics for Schrödinger maps through the so-called Hasimoto transformation. 相似文献
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We study the existence and completeness of the wave operators Wω(A(b),-Δ) for general Schrodinger operators of the form is a magnetic potential. 相似文献
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Satoko Sugano 《Mathematische Nachrichten》2016,289(14-15):1946-1960
We consider higher order Schrödinger type operators with nonnegative potentials. We assume that the potential belongs to the reverse Hölder class which includes nonnegative polynomials. We show that an operator of higher order Schrödinger type is a Calderón–Zygmund operator. We also show that there exist potentials which satisfy our assumptions but are not nonnegative polynomials. 相似文献
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Numerical solutions of nonlinear fractional Schrödinger equations using nonstandard discretizations 下载免费PDF全文
Nasser H. Sweilam Taghreed A. Assiri Muner M. Abou Hasan 《Numerical Methods for Partial Differential Equations》2017,33(5):1399-1419
In this article, numerical study for both nonlinear space‐fractional Schrödinger equation and the coupled nonlinear space‐fractional Schrödinger system is presented. We offer here the weighted average nonstandard finite difference method (WANSFDM) as a novel numerical technique to study such kinds of partial differential equations. The space fractional derivative is described in the sense of the quantum Riesz‐Feller definition. Stability analysis of the proposed method is studied. To show that this method is reliable and computationally efficient different numerical examples are provided. We expect that the proposed schemes can be applicable to different systems of fractional partial differential equations. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1399–1419, 2017 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(2):606-614
In this article, we study the increasing stability property for the determination of the potential in the Schrödinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat, and homogeneous boundary condition is prescribed on this part. In contrast to earlier works, we are able to deal with the case when potentials have some Sobolev regularity and also need not be compactly supported inside the domain. 相似文献
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Bruno Bongioanni Adrián Cabral Eleonor Harboure 《Mathematische Nachrichten》2016,289(11-12):1341-1369
A critical radius function ρ assigns to each a positive number in a way that its variation at different points is somehow controlled by a power of the distance between them. This kind of function appears naturally in the harmonic analysis related to a Schrödinger operator with V a non‐negative potential satisfying some specific reverse Hölder condition. For a family of singular integrals associated with such critical radius function, we prove boundedness results in the extreme case . On one side we obtain weighted weak (1, 1) results for a class of weights larger than Muckenhoupt class A1. On the other side, for the same weights, we prove continuity from appropriate weighted Hardy spaces into weighted L1. To achieve the latter result we define weighted Hardy spaces by means of a ρ‐localized maximal heat operator. We obtain a suitable atomic decomposition and a characterization via ρ‐localized Riesz Transforms for these spaces. For the case of ρ derived from a Schrödinger operator, we obtain new estimates for many of the operators appearing in 27 . 相似文献
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Pietro d'Avenia Marco Squassina Marianna Zenari 《Mathematical Methods in the Applied Sciences》2015,38(18):5207-5216
By means of nonsmooth critical point theory, we obtain existence of infinitely many weak solutions of the fractional Schrödinger equation with logarithmic nonlinearity. We also investigate the Hölder regularity of the weak solutions. Copyright © 2015 JohnWiley & Sons, Ltd 相似文献