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arXiv · 2408.01873

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

Andrey Badanin·Evgeny Korotyaev
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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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Andrey Badanin, Evgeny Korotyaev. 2024-08-03. Inverse problem for the L-operator in the Lax Pair of the Boussinesq equation on the circle. https://arxiv.org/abs/2408.01873

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