Inverse Scattering Transform 3-wave equations Lax representation Spectral Theory Fundamental Analytic Solutions
Issue Date:
2012
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 21, No 1, (2012), 217p-236p
Abstract:
The inverse scattering transform for a special case of the 3- wave resonant interaction equations with non-vanishing boundary conditions is studied. The Jost solutions and the fundamental analytic solutions (FAS) for the associated spectral problem are constructed. The inverse scattering problem for the Lax operator is formulated as a Riemann-Hilbert problem on a Riemannian surface. The spectral properties of the Lax operator are formulated.
