D J Kaup and Jianke Yang 2009 Inverse Problems 25 105010 doi:10.1088/0266-5611/25/10/105010
D J Kaup1 and Jianke Yang2
Show affiliationsWe 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.
Issue 10 (October 2009)
Received 30 June 2009, in final form 11 August 2009
Published 16 September 2009
D J Kaup and Jianke Yang 2009 Inverse Problems 25 105010
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C Leighton et al 2007 J. Phys.: Condens. Matter 19 315219
V K Aswal et al 2007 J. Phys.: Condens. Matter 19 116101
Ming Zhao et al 2009 J. Phys.: Conf. Ser. 188 012020
A Bernardi et al 2007 Nanotechnology 18 475401
Tomoaki Nogawa and Takehisa Hasegawa 2009 J. Phys. A: Math. Theor. 42 145001
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