Article Dans Une Revue Journal of Physics A General Physics (1968-1972) Année : 2001

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

Résumé

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.

Dates et versions

hal-00178208 , version 1 (10-10-2007)

Identifiants

Citer

J. Leon, A. Spire. The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications. Journal of Physics A General Physics (1968-1972), 2001, 34, pp.7539-7380. ⟨10.1088/0305-4470/34/36/316⟩. ⟨hal-00178208⟩
29 Consultations
0 Téléchargements

Altmetric

Partager

  • More