The inverse scattering transform and squared eigenfunctions for a degenerate 3 × 3 operator

We present the covering set of the squared eigenfunctions for a degenerate 3 × 3 eigenvalue problem. The derivation follows the approach recently outlined by Yang and Kaup on this same equation (J. Math. Phys. 50 023504 (2009)). This eigenvalue problem is important since it serves as the spectral problem for the inverse scattering transform (IST) of the vector NLS equation, the Sasa–Satsuma equation, and a degenerate two-level Maxwell–Bloch system. The use of this covering set would allow one to treat the linear perturbations of these equations in a common and systematic manner. Comparison with previous results on the perturbed continuous spectrum of the Sasa–Satsuma equation is made.

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