Inverse problem for the L-operator in the Lax Pair of the Boussinesq equation on the circle

2024/08/03 by Andrey Badanin, Badanin, Andrey, Evgeny Korotyaev +1
Mathematics · #34L20 #34L40 #47E05 #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2408.01873

openalex publication_date 2024/08/03 · openalex created_date 2024/10/14 · openalex updated_date 2026/07/28

Abstract

We consider a third-order non-self-adjoint operator, which is an L-operator in the Lax pair for the Boussinesq equation on the circle. We construct a mapping from the set of operator coefficients to the set of spectral data, similar to the corresponding mapping for the Hill operator constructed by E. Korotyaev. We prove that in a neighborhood of zero our mapping is analytic and one-to-one.

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