Inverse problem for 3-rd order operators under the 3-point Dirichlet conditions

2024/08/03 by Andrey Badanin, Badanin, Andrey, Evgeny Korotyaev +1
Mathematics · #34L20 #34L40 #47E05 #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2408.01886

openalex publication_date 2024/08/03 · openalex created_date 2025/01/17 · openalex updated_date 2026/07/28

Abstract

We solve an inverse problem for a third order differential operator under the 3-point Dirichlet conditions. The third-order operator is an L-operator in the Lax pair for the good Boussinesq equation. We construct the mapping from the set of the coefficients to the set of spectral data. This mapping is an analytic bijection on a neighborhood of the zero.

Related

• Inverse problem for the L-operator in the Lax Pair of the Boussinesq equation on the circle
• Third order operators with three-point conditions associated with Boussinesq's equation
• Inverse spectral problem for the third-order differential equation
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• Inverse spectral problem for a third-order differential operator