Existence of generalized translation operators from the Agranovitch-Marchenko transformation (Jost solutions)

Coz, Marcel; Coudray, C.

doi:10.1063/1.1666228

Cited by 8 publications

(4 citation statements)

References 8 publications

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“…where K ℓ (r, r ′ ) and A ℓ (r, r ′ ) are the kernels of the integral equation. K ℓ (r, r ′ ) is related to the potential V (r) through a hyperbolic differential equation [33,34]. A ℓ (r, r ′ ) is computed from the continuum and discrete spectra as follows [35][36][37][38][39]:…”

Section: Gel'fand-levitan-marchenko Theorymentioning

confidence: 99%

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Meoto

Lekala

2019

J. Phys. Commun.

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Potentials are constructed for the lambda-nucleon interaction in the S 1 0 and S 3 1 channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel'fand-Levitan-Marchenko theory. Experimental data with good statistics is not available for lambda-nucleon scattering. This leaves theoretical scattering phases as the only option through which the rigorous theory of quantum inverse scattering can be used in probing the lambda-nucleon force. Using rational-function interpolations on the theoretical scattering data, the kernels of the Gel'fand-Levitan-Marchenko integral equation become degenerate, resulting in a closed-form solution. The new potentials restored, which are shown to be unique through the Levinson theorem, bear the expected features of short-range repulsion and intermediate-range attraction. Charge symmetry breaking, which is perceptible in the scattering phases, is preserved in the new potentials. The lambdanucleon force in the S 1 0 channel is observed to be stronger than in the S 3 1 channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schrödinger calculations.

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Section: Gel'fand-levitan-marchenko Theorymentioning

confidence: 99%

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Meoto

Lekala

2019

J. Phys. Commun.

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“…Most skillfully, they were able to create generalized translation operators (GTO) and from a key paper entitled Existence of generalized translation operators from the Agranovitch-Marchenko transformation. Along with Marcel Coz and Christine Coudray the names, Levitan, Agranovich, Marchenko, Faddeev, Newton, and Sabatier [42][43][44][45][46][47][48] are often cited in reports on inversion mathematics and physics. Jacques , Marcel Coz, and Christine Coudray, along with many others, are testament to the excellent mathematical education and training in France.…”

Section: Introduction and Surveymentioning

confidence: 99%

Intricate partial waves in nuclear scattering

Geramb

Viktor²

2020

Eur. Phys. J. A

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This article is meant as an encomium of the life-span endeavor of Jacques Raynal to relate nuclear scattering density matrices with numerical methods. The mathematical investigations he made involved intricate hypergeometric coupling algebras and transformations. He was among the first to appreciate the general importance of these studies. His efforts over 60 years are most praiseworthy and, for them, Jacques has gained much respect.

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“…The value of such a property means that Riemann's method continues to draw the attention of investigators today. Some applications include solving electromagnetic problems exhibiting rotational symmetry [1], finding existence criteria for the eigenvalues of the solution of focal point problems [2], solving for the solution of transient plane waves [3] and the inverse problem of scattering theory [4]- [12]. More recently, Riemann's method has been applied to the solution of coupled Korteweg-de Vries equations [13], to boundary value problems for the non-homogeneous wave equation [14]- [18], to the solution of the non-linear Schrödinger equation [19]- [20] and modelling hyperbolic quasi-linear equations [21]- [23].…”

Section: Introductionmentioning

confidence: 99%

On The Riemann Function

Zeitsch¹

2018

Preprint

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Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

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Existence of generalized translation operators from the Agranovitch-Marchenko transformation (Jost solutions)

Cited by 8 publications

References 8 publications

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Intricate partial waves in nuclear scattering

On The Riemann Function

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