On the 3-wave Equations with Constant Boundary Conditions

Details On the 3-wave Equations with Constant Boundary Conditions On the 3-wave Equations with Constant Boundary Conditions

2012-04-24

arxiv.org/abs/1204.5346v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, LaTeX, 2 EPS figures

Scientific paper

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.

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