English

Inverse scattering for reflectionless Schr\"odinger operators with integrable potentials and generalized soliton solutions for the KdV equation

Spectral Theory 2020-06-24 v1 Mathematical Physics math.MP

Abstract

We give a complete characterisation of the reflectionless Schr\"odinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such potentials from the eigenvalues and norming constants, and derive the corresponding generalized soliton solutions of the Korteweg--de Vries equation

Keywords

Cite

@article{arxiv.2006.12782,
  title  = {Inverse scattering for reflectionless Schr\"odinger operators with integrable potentials and generalized soliton solutions for the KdV equation},
  author = {Rostyslav Hryniv and Bohdan Melnyk and Yaroslav Mykytyuk},
  journal= {arXiv preprint arXiv:2006.12782},
  year   = {2020}
}

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35 pages