Geodesic
Mc'Kean's transformation for 3-rd order operators
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 44-54

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We consider a non-self-adjoint third order operator with 1-periodic coefficients. Integrating the Boussinesq equation on a circle requires solving the inverse spectral problem for this operator. In 1981, McKean introduced a transformation that reduces the spectral problem for this operator to the spectral problem for the Hill operator with a potential that depends analytically on the energy. In the present paper we are studying this transformation. 
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     author = {A. V. Badanin and E. L. Korotyaev},
     title = {Mc'Kean's transformation for 3-rd order operators},
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A. V. Badanin; E. L. Korotyaev. Mc'Kean's transformation for 3-rd order operators. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 44-54. http://geodesic.mathdoc.fr/item/ZNSL_2024_533_a2/