Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus
Analysis of PDEs
2023-01-11 v1 Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.2301.03919,
title = {Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus},
author = {Louise Gassot},
journal= {arXiv preprint arXiv:2301.03919},
year = {2023}
}