On the 3-wave Equations with Constant Boundary Conditions
Exactly Solvable and Integrable Systems
2013-02-12 v2 Mathematical Physics
math.MP
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 Riemann surface. The spectral properties of the Lax operator are formulated.
Cite
@article{arxiv.1204.5346,
title = {On the 3-wave Equations with Constant Boundary Conditions},
author = {Vladimir S. Gerdjikov and Georgi G. Grahovski},
journal= {arXiv preprint arXiv:1204.5346},
year = {2013}
}
Comments
15 pages, LaTeX, 2 EPS figures