SIMPLICITY AND FINITENESS OF DISCRETE SPECTRUM OF THE BENJAMIN-ONO SCATTERING OPERATOR

被引：13

作者：

Wu, Yilun ^{[1
]}

机构：

[1] Brown Univ, Dept Math, Providence, RI 02912 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2016年 / 48卷 / 02期

关键词：

Benjamin-Ono; inverse scattering transform; spectral analysis; Birman-Schwinger; discrete spectrum; Fokas-Ablowitz; KORTEWEG-DEVRIES EQUATION; SMALL DISPERSION LIMIT; DE-VRIES EQUATION; INTERNAL WAVES; WELL-POSEDNESS; CAUCHY-PROBLEM; TRANSFORM; FLUIDS;

D O I：

10.1137/15M1030649

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A spectral analysis is done on the L operator of the Lax pair for the Benjamin-Ono equation. Simplicity and finiteness of the discrete spectrum are established as are needed for the Fokas and Ablowitz inverse scattering transform scheme. A crucial step in the simplicity proof is the discovery of a new identity connecting the L-2 norm of the eigenvector to its inner product with the scattering potential. The proof for finiteness is an extension of the ideas involved in the Birman-Schwinger bound for Schrodinger operators.

引用

页码：1348 / 1367

页数：20

共 33 条

[1]

[Anonymous], 1975, PUBL RES I MATH SCI, DOI DOI 10.2977/PRIMS/1195192000

[2]

[Anonymous], THESIS U MICHIGAN

[3] INTERNAL WAVES OF PERMANENT FORM IN FLUIDS OF GREAT DEPTH [J].