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LAX EIGENVALUES IN THE ZERO-DISPERSION LIMIT FOR THE BENJAMIN-ONO EQUATION ON THE TORUS.
- Source :
-
SIAM Journal on Mathematical Analysis . 2023, Vol. 55 Issue 5, p5782-5822. 41p. - Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 55
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 173615379
- Full Text :
- https://doi.org/10.1137/23M154635X