共查询到20条相似文献,搜索用时 15 毫秒
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By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classic Toda lattice equation,the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases.The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform. 相似文献
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Starting with the group of operators on a separable Hilbert space that differ from the identity by a trace-class operator,
we construct a solution of the two-dimensional infinite Toda hierarchy associated with a maximal commutative subalgebra in
complex k×k matrices.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 177–192, April, 2008. 相似文献
4.
LIU XiaoJun & GAO Can 《中国科学 数学(英文版)》2011,(2)
In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the pe... 相似文献
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R. G. Novikov 《Selecta Mathematica, New Series》1997,3(2):245-302
We consider the Dirac-ZS-AKNS system (1) where (the space of functions with n derivatives in L
1), (2) We consider for (1) the transition matrix and, in addition, for the case of the Dirac system (i.e. for the selfadjoint case the scattering matrix We can divide main results of the present work into three parts. I. We show that the inverse scattering transform and the inverse Fourier transform give the same solution, up to smooth functions,
of the inverse scattering problem for (1). More preciseley, we show that, under condition (2) with , the following formulas are valid: (3) and, in addition, for the case of the Dirac system (4) where denotes the factor space. II. Using (3), (4), we give the characterization of the transition matrix and the scattering matrix for the case of the Dirac
system under condition (2) with
III. As applications of the results mentioned above, we show that 1) for any real-valued initial data , the Cauchy problem for the sh-Gordon equation has a unique solution such that and for any t > 0, 2) in addition, for , for such a solution the following formula is valid: where
denotes the space of functions locally integrable with n derivatives. We give also a review of preceding results. 相似文献
6.
A. Kh. Khanmamedov 《Theoretical and Mathematical Physics》2005,142(1):1-7
We prove the existence of a rapidly decreasing solution of the Cauchy problem for the Toda lattice. We find a class of initial data guaranteeing the existence of such a solution.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 5–12, January, 2005. 相似文献
7.
The one-dimensional Schrödinger equation is considered when the potential is real valued and integrable and has a finite first moment. The recovery of such a potential is analyzed in terms of the scattering data consisting of a reflection coefficient, all the bound-state energies, knowledge of the potential on a finite interval, and all of the bound-state norming constants except one. It is shown that a missing norming constant in the data can cause at most a double nonuniqueness in the recovery. In the particular case when the missing norming constant in the data corresponds to the lowest-energy bound state, the necessary and sufficient conditions are obtained for the nonuniqueness, and the two norming constants and the corresponding potentials are determined. Some explicit examples are provided to illustrate the nonuniqueness. 相似文献
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G. U. Urazboev 《Theoretical and Mathematical Physics》2008,154(2):260-269
We describe a method for integrating the Toda lattice with a self-consistent source using the inverse scattering method for
a discrete Sturm-Liouville operator with moving eigenvalues.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 305–315, February, 2008. 相似文献
10.
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
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The Ragnisco-Tu hierarchy with self-consistent sources is derived. The exact solutions of the hierarchy are obtained via the inverse scattering transform (IST). An explicit form for a solution of the Ragnisco-Tu equation is presented. 相似文献
12.
We use p-component fermions, p = 2, 3,..., to represent (2p−2)N-fold integrals as a fermionic vacuum expectation. This yields
a fermionic representation for various (2p−2)-matrix models. We discuss links with the p-component Kadomtsev-Petviashvili
hierarchy and also with the p-component Toda lattice hierarchy. We show that the set of all but two flows of the p-component
Toda lattice hierarchy changes standard matrix models to new ones.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 265–277, August, 2007. 相似文献
13.
We show that fixed energy scattering measurements for the magnetic Schrödinger operator uniquely determine the magnetic field and electric potential in dimensions n?3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston (1995) [5] which considered potentials with many derivatives. The proof is close to arguments in inverse boundary problems, and is based on constructing complex geometrical optics solutions to the Schrödinger equation via a pseudodifferential conjugation argument. 相似文献
14.
We study the topology of the isospectral real manifold of the
periodic Toda lattice consisting of 2
N–1 different systems. The solutions of these systems contain blow-ups, and the set of these singular points defines a divisor of the manifold. With the divisor added, the manifold is compactified as the real part of the (N–1)-dimensional Jacobi variety associated with a hyperelliptic Riemann surface of genus g=N–1. We also study the real structure of the divisor and provide conjectures on the topology of the affine part of the real Jacobian and on the gluing rule over the divisor to compactify the manifold based on the sign representation of the Weyl group of
. 相似文献
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Mikló s Horvá th 《Transactions of the American Mathematical Society》2006,358(11):5161-5177
Recently A. G. Ramm (1999) has shown that a subset of phase shifts , , determines the potential if the indices of the known shifts satisfy the Müntz condition . We prove the necessity of this condition in some classes of potentials. The problem is reduced to an inverse eigenvalue problem for the half-line Schrödinger operators.
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In this work we develop the inverse scattering transform (IST) for the defocusing Ablowitz–Ladik (AL) equation with arbitrarily a large nonzero background at space infinity. The IST was developed in previous works under the assumption that the amplitude of the background satisfies a “small norm” condition . On the other hand, Ohta and Yang recently showed that the defocusing AL system, which is modulationally stable for , becomes unstable if , and exhibits discrete rogue wave solutions, some of which are regular for all times. Here, we construct the IST for the defocusing AL with , analyze the spectrum, and characterize the soliton and rational solutions from a spectral point of view. We formulate the direct and inverse problems by using a suitable uniformization variable, and pose the inverse problem as an RHP across a simple contour in the complex plane of the uniform variable. As a by‐product of the IST, we also obtain explicit soliton solutions, which are the discrete analog of the celebrated Kuznetsov–Ma, Akhmediev, Peregrine solutions, and which mimic the corresponding solutions for the focusing AL equation. Soliton solutions that are the analog of the dark soliton solutions of the defocusing AL equation in the case are also presented. 相似文献
18.
Francois NICOLEAU 《数学学报(英文版)》2006,22(5):1485-1492
We consider a pair of Hamiltonians (H, H0) on L2(R^n), where H0=p^2 -x^2 is a SchrSdinger operator with a repulsive potential, and H = H0+V(x). We show that, under suitable assumptions on the decay of the electric potential, V is uniquely determined by the high energy limit of the scattering operator. 相似文献
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Xiao Bao Zhu 《数学学报(英文版)》2011,27(8):1501-1520
In this paper, we study the solutions for Toda system on Riemann surface with boundary. We prove a sufficient condition for
the existence of solution of Toda system in the critical case. 相似文献
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The inverse scattering transform method for the dimensionally reduced self-dual equations of the Yang-Mills fields (Zakharov-Manakov
system) is developed. Reductions on the scattering data are obtained. The resolvent theory for the auxiliary linear problem
is developed. Dispersion relations and trace identities are presented. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 150–167
Translated by B. M. Bekker. 相似文献