A Zakharov-Shabat inverse scattering problem with a polynomial spectral dependence in the potential期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A Zakharov-Shabat inverse scattering problem with a polynomial spectral dependence in the potential

Authors:	M O Guillaume M Jaulent

Institution:	(1) Département de Physique Mathématique, Université des Sciences et Techniques du Languedoc, 34060 Montpellier Cedex, France

Abstract:	The inverse scattering problem for the Zakharov-Shabat system $y^\prime + iK\sigma _3 y = \left {\sum\nolimits_{p = 0}^n {(\sqrt{2n}]{K})^p \upsilon } _p (x)} \right]y, x \in \mathbb{R}$ , is considered. It is solved by reduction to the inverse scattering problem for two coupled Zakharov-Shabat systems in a 4n-dimensional space: $y^{ \pm \prime } + iK(\sigma _3 \otimes I_{2n} )y^ \pm = (U^ \pm \pm KQ^ \pm )y^ \pm (x \in \mathbb{R})$ . This work has been done as part of the program ‘Recherche Coopérative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses’. Physique Mathématique et Théorique, Equipe de recherche associée au CNRS, No. 154.

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