Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus

2023/01/10 by Louise Gassot, Gassot, Louise
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · pdf · doi:10.48550/arxiv.2301.03919

openalex publication_date 2023/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the zero-dispersion limit for the Benjamin-Ono equation on the torus for bell shaped initial data. Using the approximation by truncated Fourier series, we transform the eigenvalue equation for the Lax operator into a problem in the complex plane. Then, we use the steepest descent method to get asymptotic expansions of the Lax eigenvalues. As a consequence, we determine the weak limit of solutions as the dispersion parameter goes to zero, as long as the initial data is an even bell shaped potential.

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