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Semiclassical Eigenvalue Distribution of the ZakharovShabat Eigenvalue Problem.
 Phys. D
, 1996
"... In this paper consider the semiclassical limit of the non selfadjoint ZakharovShabat eigenvalue problem. We conduct a series of careful numerical experiments which provide strong evidence that the number of eigenvalues scales like ffl \Gamma1 , just as in the selfadjoint case, and that the eigen ..."
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Cited by 21 (0 self)
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In this paper consider the semiclassical limit of the non selfadjoint ZakharovShabat eigenvalue problem. We conduct a series of careful numerical experiments which provide strong evidence that the number of eigenvalues scales like ffl \Gamma1 , just as in the selfadjoint case
Estimates on periodic and Dirichlet eigenvalues for the ZakharovShabat system
, 2000
"... Consider the 2 \Theta 2 first order system due to ZakharovShabat, LY := i ` 1 0 0 \Gamma1 ' Y 0 + ` 0 / 1 / 2 0 ' Y = Y with / 1 ; / 2 being complex valued functions of period one in the weighted Sobolev space H w j H w C : Denote by spec(/ 1 ; / 2 ) the set of periodic eig ..."
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Consider the 2 \Theta 2 first order system due to ZakharovShabat, LY := i ` 1 0 0 \Gamma1 ' Y 0 + ` 0 / 1 / 2 0 ' Y = Y with / 1 ; / 2 being complex valued functions of period one in the weighted Sobolev space H w j H w C : Denote by spec(/ 1 ; / 2 ) the set of periodic
Semiclassical Eigenvalue Distribution of the Non SelfAdjoint ZakharovShabat Eigenvalue Problem.
, 1995
"... In this paper we review the theory of the semiclassical limit of the non selfadjoint ZakharovShabat eigenvalue problem. We conduct a series of careful numerical experiments which provide strong evidence that the number of eigenvalues scales like ffl \Gamma1 , just as in the selfadjoint case, and ..."
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In this paper we review the theory of the semiclassical limit of the non selfadjoint ZakharovShabat eigenvalue problem. We conduct a series of careful numerical experiments which provide strong evidence that the number of eigenvalues scales like ffl \Gamma1 , just as in the selfadjoint case
On the dressing method for the generalised ZakharovShabat system
 Nuclear Physics B
"... The dressing procedure for the Generalised ZakharovShabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed ’ fundamental analytica ..."
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Cited by 7 (1 self)
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The dressing procedure for the Generalised ZakharovShabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed ’ fundamental
Inverse Problem and Estimates for Periodic ZakharovShabat Systems
, 2000
"... Consider the ZakharovShabat (or Dirac) operator T zs on L 2 (R) \Phi L 2 (R) with real periodic vector potential q = (q 1 ; q 2 ) 2 H = L 2 (T) \Phi L 2 (T). The spectrum of T zs is absolutely continuous and consists of intervals separated by gaps (z \Gamma n ; z + n ); n 2 Z. ?From ..."
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Cited by 7 (4 self)
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the Dirichlet eigenvalues m n ; n 2 Z of the ZakharovShabat equation with Dirichlet boundary conditions at 0; 1, the center of the gap and the square of the gap length we construct the gap length mapping g : H ! ` 2 \Phi` 2 . Using nonlinear functional analysis in Hilbert spaces, we show that this mapping
MARCHENKO EQUATIONS AND NORMING CONSTANTS OF THE MATRIX ZAKHAROV–SHABAT SYSTEM
"... (communicated by A. Ran) Abstract. In this article we derive the Marchenko integral equations for solving the inverse scattering problem for the matrix ZakharovShabat system with a potential without symmetry properties and having L1 entries under a technical hypothesis preventing the accumulation o ..."
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(communicated by A. Ran) Abstract. In this article we derive the Marchenko integral equations for solving the inverse scattering problem for the matrix ZakharovShabat system with a potential without symmetry properties and having L1 entries under a technical hypothesis preventing the accumulation
On the Location of the Discrete Eigenvalues for Defocusing ZakharovShabat Systems having Potentials with Nonvanishing Boundary Conditions
"... Abstract. In this article we prove that the discrete eigenvalues of the ZakharovShabat system belong to certain neighborhoods of the endpoints of the spectral gap and the discrete eigenvalue of the free Hamiltonian. 1. ..."
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Abstract. In this article we prove that the discrete eigenvalues of the ZakharovShabat system belong to certain neighborhoods of the endpoints of the spectral gap and the discrete eigenvalue of the free Hamiltonian. 1.
Integral Equations and Operator Theory Scattering Operators for Matrix ZakharovShabat Systems
"... Abstract. In this article the scattering matrix pertaining to the defocusing matrix ZakharovShabat system on the line is related to the scattering operator arising from timedependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing ..."
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Abstract. In this article the scattering matrix pertaining to the defocusing matrix ZakharovShabat system on the line is related to the scattering operator arising from timedependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing
Results 1  10
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2,239