Abstract
A new and simpler construction of the family of rational solutions of the Korteweg-deVries equation is given. This construction is related to a factorization of the Sturm-Liouville operators into first order operators and a new deformation problem for the latter. In the final section the spectral representation for the corresponding complex potentials is discussed.
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Communicated by J. Moser
This work was partially sponsored by the National Science Foundation, Grants MCS 77-01986 DMM3, MCS 75-17385, and by the United States Army under Contract No. DAAG29-75-C-0024
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Adler, M., Moser, J. On a class of polynomials connected with the Korteweg-deVries equation. Commun.Math. Phys. 61, 1–30 (1978). https://doi.org/10.1007/BF01609465
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DOI: https://doi.org/10.1007/BF01609465