共查询到20条相似文献,搜索用时 31 毫秒
1.
E. I. Galakhov 《Mathematical Notes》2012,92(3-4):333-344
We obtain conditions for the existence and blow-up of global solutions of systems of nonlinear wave equations with compactly supported initial data and critical nonlinearities arising from the scattering theory of electromagnetic waves. 相似文献
2.
Multiparametric dissipative linear stationary dynamical scattering systems: Discrete case, II: Existence of conservative dilations 总被引:1,自引:0,他引:1
Dmitriy S. Kalyuzhniy 《Integral Equations and Operator Theory》2000,36(1):107-120
In the present paper we introduce the notion of dilation of a multiparametric linear stationary dynamical system (systems of this type, in particular dissipative, and conservative scattering ones were first introduced in [6]). We establish the criterion for existence of a conservative dilation of a multiparametric dissipative scattering system. This allows to distinguish the class of so-calledN-dissipative systems preserving the most important properties of one-parametric dissipative scattering systems.Research supported in part by the Ukrainian-Israeli project of scientific co-operation (contract no. 2M/1516-97). 相似文献
3.
Do Kong Khan 《Ukrainian Mathematical Journal》1990,42(4):432-437
By the method of functional models of operators and systems one proves necessary and sufficient conditions in order that a step-by-step combination of n minimal passive scattering systems be a minimal system.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 488–494, April, 1990. 相似文献
4.
Mansur I. Ismailov 《Journal of Mathematical Analysis and Applications》2010,365(2):498-509
In this paper the forward and inverse scattering problems for the nonstationary Dirac-type systems on the plane are considered. The scattering data for the inverse scattering problem (ISP) is defined and a unique restoration of the potential from the scattering data is proved. 相似文献
5.
Scattering Systems with Several Evolutions and Multidimensional Input/State/Output Systems 总被引:1,自引:0,他引:1
Joseph A. Ball Cora Sadosky Victor Vinnikov 《Integral Equations and Operator Theory》2005,52(3):323-393
The one-to-one correspondence between one-dimensional linear (stationary, causal) input/state/output systems and scattering systems with one evolution operator, in which the scattering function of the scattering system coincides with the transfer function of the linear system, is well understood, and has significant applications in H∞ control theory. Here we consider this correspondence in the d-dimensional setting in which the transfer and scattering functions are defined on the polydisk. Unlike in the onedimensional case, the multidimensional state space realizations and the corresponding multi-evolution scattering systems are not necessarily equivalent, and the cases d = 2 and d > 2 differ substantially. A new proof of Andô’s dilation theorem for a pair of commuting contraction operators and a new statespace realization theorem for a matrix-valued inner function on the bidisk are obtained as corollaries of the analysis. 相似文献
6.
Given a normally hyperbolic invariant manifold Λ for a map f, whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an asymptotic orbit in the past, gives the asymptotic orbit in the future.We show that when f and Λ are symplectic (respectively exact symplectic) then, the scattering map is symplectic (respectively exact symplectic). Furthermore, we show that, in the exact symplectic case, there are extremely easy formulas for the primitive function, which have a variational interpretation as difference of actions.We use this geometric information to obtain efficient perturbative calculations of the scattering map using deformation theory. This perturbation theory generalizes and extends several results already obtained using the Melnikov method. Analogous results are true for Hamiltonian flows. The proofs are obtained by geometrically natural methods and do not involve the use of particular coordinate systems, hence the results can be used to obtain intersection properties of objects of any type.We also reexamine the calculation of the scattering map in a geodesic flow perturbed by a quasi-periodic potential. We show that the geometric theory reproduces the results obtained in [Amadeu Delshams, Rafael de la Llave, Tere M. Seara, Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows, Adv. Math. 202 (1) (2006) 64-188] using methods of fast-slow systems. Moreover, the geometric theory allows to compute perturbatively the dependence on the slow variables, which does not seem to be accessible to the previous methods. 相似文献
7.
High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localization at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems that resonate in a subwavelength regime. Our from-first-principles asymptotic analysis yields a characterization in terms of the generalized capacitance matrix, giving a discrete approximation of the three-dimensional scattering problem. We develop landscape theory for the generalized capacitance matrix and use it to predict the positions of three-dimensional wave focusing and localization in random and non-periodic systems of subwavelength resonators. 相似文献
8.
It is shown how the same mathematical technique can be usedto solve a number of different problems all concerned with thesame geometry. The multipole method, which can be thought ofas an extension of separation of variables to problems wherethe boundaries lie on the coordinate surfaces of two differentcoordinate systems, is used to solve the problems of potentialflow, Stokes flow, and acoustic scattering for the case of asphere situated on the axis of a circular cylindrical tube. 相似文献
9.
A numerical-analytic method employing series over basis systems of propagating and edge standing normal waves is used to study dynamic edge effects in the scattering of the lowest order travelling wave at the contact surface between two semi-infinite components of a prismatic waveguide with a rectangular cross section made of single crystals of Rochelle salt and sodium ammonium selenate dihydrate. 相似文献
10.
Criterion of unitary similarity of minimal passive scattering systems with a given transfer function
We establish necessary and sufficient conditions under which all minimal passive scattering systems that have a given transfer
operator function are unitarily equivalent. These conditions can be significantly simplified in special cases important for
applications, in particular, in the case where a transfer function is rational and in a more general case where this function
is pseudoextendable. 相似文献
11.
On the positive semi‐infinite interval, we obtained a generalization of the Marchenko method for a Dirac equation system with a discontinuous coefficient and a quadratic polynomial on a spectral parameter in the boundary condition. In this connection, we use an new integral representation of the Jost solution of equation systems, which does not have a ‘triangular’ form. The scattering function of the problem is defined, and its properties are examined. The Marchenko‐type main equation is obtained, and it is shown that the potential is uniquely recovered in terms the scattering function. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
Tommy Dreyfus 《Journal of Mathematical Analysis and Applications》1978,64(1):114-134
For a large class of scattering systems we study the behavior of the determinant of the scattering matrix as a function on the spectrum of the unperturbed operator. The variation of this determinant is related to the number of eigenvalues due to the perturbation. This relation generalizes results of Levinson and others. The range of physical systems to which these results apply is thus considerably extended. 相似文献
13.
V. V. Popuzin M. A. Sumbatyan R. A. Tanyushin 《Computational Mathematics and Mathematical Physics》2013,53(8):1195-1206
A new iteration method is proposed for the wave equation describing the scattering of a harmonic wave from an arbitrary configuration in the form of an array of thin straight barriers. The problem is reduced to a system of boundary integral equations, which are discretized by applying the Belotserkovskii-Lifanov method. In discrete form, a finite number of systems with Toeplitz matrices (the number of systems is equal to the number of barriers) are solved at each iteration step by applying special fast methods. The algorithm is tested on several geometries, and its convergence in these cases is analyzed. 相似文献
14.
smail Hakk Tayyar Serkan Aksoy Ali Alkumru 《Mathematical Methods in the Applied Sciences》2005,28(5):525-549
The electromagnetic scattering of the surface wave by a rectangular impedance cylinder located on an infinite reactive plane is considered for the case that the impedances of the horizontal and vertical sides of the cylinder can have different values. Firstly, the diffraction problem is reduced into a modified Wiener–Hopf equation of the third kind and then solved approximately. The solution contains branch‐cut integrals and two infinite sets of constants satisfying two infinite systems of linear algebraic equations. The approximate analytical or numerical evaluations of corresponding integrals and numerical solution of the linear algebraic equation systems are obtained for various values of parameters such as the surface reactance of the plane, the vertical and horizontal wall impedances, the width and the height of the cylinder. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
Bitangential input scattering problems are formulated and analyzed for canonical integral systems. Special attention is paid to the case when the input scattering matrix is ap×q matrix valued function of Wiener class. Formulas for the solution of the inverse input scattering problem are obtained by reproducing kernel Hilbert space methods. A number of illustrative examples are presented. Additional examples for the case when the input scattering matrix is of Wiener class/rational will be presented in a future publication. 相似文献
16.
17.
《Journal of Functional Analysis》1986,67(1):73-104
We study the spectral and scattering problems for symmetric systems of nonconstant deficit. We prove (i) discreteness of eigenvalues, (ii) absolute continuity of continuous spectrum. (iii) principle of limiting absorption. As an application to the scattering problems, the decay of local energy and the completeness of wave operators are obtained. The class of systems we consider here includes the linearized equation of magnetohydrodynamics as a typical example. 相似文献
18.
The influence of a fermionic impurity on the spectrum of overcondensate excitations of a superfluid Bose system is investigated. The scattering of neutrons on the Bose condensate of a superfluid 4He and a mixture of the liquid 3He and 4He is considered. An analytic expression for the spectrum of overcondensate excitations for these two systems is found. Bibliography: 10 titles. 相似文献
19.
We discuss the application of an augmented conjugate gradient to the solution of a sequence of linear systems of the same
matrix appearing in an iterative process for the solution of scattering problems. The conjugate gradient method applied to
the first system generates a Krylov subspace, then for the following systems, a modified conjugate gradient is applied using
orthogonal projections on this subspace to compute an initial guess and modified descent directions leading to a better convergence.
The scattering problem is treated via an Exact Controllability formulation and a preconditioned conjugate gradient algorithm
is introduced. The set of linear systems to be solved are associated to this preconditioning. The efficiency of the method
is tested on different 3D acoustic problems.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
S. A. Kuzhel’ 《Ukrainian Mathematical Journal》1998,50(12):1844-1859
We give the definition of ρ-perturbations of an abstract wave equation. As a special case, this definition includes perturbations with compact support for the classical wave equation. By using the Lax-Phillips method, we study scattering of “ρ-perturbed” systems and establish some properties of corresponding scattering matrices. 相似文献