English

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.

Keywords

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

R2 v1 2026-06-21T20:53:59.803Z