2020•arXiv (Cornell University)Open access
Inverse scattering for reflectionless Schr\\"odinger operators with\n integrable potentials and generalized soliton solutions for the KdV equation
Rostyslav Hryniv, Bohdan Melnyk, Yaroslav V. Mykytyuk
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Abstract
We give a complete characterisation of the reflectionless Schr\\"odinger\noperators on the line with integrable potentials, solve the inverse scattering\nproblem of reconstructing such potentials from the eigenvalues and norming\nconstants, and derive the corresponding generalized soliton solutions of the\nKorteweg--de Vries equation\n
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