Asymptotics of the divisor for the good Boussinesq equation

2024/09/17 by Andrey Badanin, Badanin, Andrey, Korotyaev, Evgeny
Mathematics · #34L20 #34L40 #47E05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.10988

openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a third order operator under the three-point Dirichlet condition. Its spectrum is the so-called auxiliary spectrum for the good Boussinesq equation, as well as the Dirichlet spectrum for the Schrödinger operator on the unit interval is the auxiliary spectrum for the periodic KdV equation. The auxiliary spectrum is formed by projections of the points of the divisor onto the spectral plane. We estimate the spectrum and the corresponding norming constants in terms of small operator coefficients. This work is the first in a series of papers devoted to solving the inverse problem for the Boussinesq equation.

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