Direct and Inverse Scattering for Skewselfadjoint Hamiltonian Systems

Mee, Cornelis van der

doi:10.1007/978-3-0348-7881-4_17

Cited by 10 publications

(17 citation statements)

References 21 publications

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“…The following proposition can be proved as its counterpart in [6,17,11]. Contrary to the practice in [6,17,11] …”

Section: B)mentioning

confidence: 97%

“…Before stating the next proposition (cf. [6,17,11]) we introduce a partitioning of square matrices of order n + m into four submatrices which have the subscripts 1, 2, 3, 4 :…”

Section: B)mentioning

confidence: 99%

“…This is also the case for the rows ofΨ(λ , x) andΦ(λ , x) . As in [6,17,11], we therefore introduce modified Jost matrices by interchanging their columns in such a way that we obtain matrices that are analytic in λ ∈ C + and λ ∈ C − , respectively.…”

Section: A Principal Parts Of Transmission Coefficientsmentioning

confidence: 99%

“…Throughout we drop the notational system of [6,11,17]. Instead, we compromise between using Jost solutions as column vectors (as in [2,3,15,18]) and Jost solutions as square matrices (as in [6,11,17]), since either notation is advantageous in different circumstances.…”

Section: Introductionmentioning

confidence: 99%

“…Instead, we compromise between using Jost solutions as column vectors (as in [2,3,15,18]) and Jost solutions as square matrices (as in [6,11,17]), since either notation is advantageous in different circumstances. We distinguish between different related entities by using overlines for those functions analytic on the upper half complex plane.…”

Section: Introductionmentioning

confidence: 99%

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Nonautonomous Exponential Dichotomy

Mee

2007

Integr. equ. oper. theory

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Abstract. In this article we derive the Marchenko integral equations for solving the inverse scattering problem for the matrix Zakharov-Shabat system with a potential without symmetry properties and having L 1 entries under a technical hypothesis preventing the accumulation of discrete eigenvalues on the continuous spectrum. We derive additional symmetry properties in the focusing case. The norming constant matrices appearing as parameter matrices in the Marchenko integral kernels are defined and studied without making any assumptions on the Jordan structure of the matrix Zakharov-Shabat Hamiltonian at the discrete eigenvalues.

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“…The following proposition can be proved as its counterpart in [6,17,11]. Contrary to the practice in [6,17,11] …”

Section: B)mentioning

confidence: 97%

“…Before stating the next proposition (cf. [6,17,11]) we introduce a partitioning of square matrices of order n + m into four submatrices which have the subscripts 1, 2, 3, 4 :…”

Section: B)mentioning

confidence: 99%

Section: A Principal Parts Of Transmission Coefficientsmentioning

confidence: 99%