The scattering transform for the Benjamin-Ono equation
- 1 October 1990
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 6 (5) , 825-861
- https://doi.org/10.1088/0266-5611/6/5/011
Abstract
The authors use constructive methods to investigate the spectral theory of the Benjamin-Ono equation. Since the linearization series used previously is singular, they replace it with an improved series obtained by finite-rank renormalization. This introduces additional scattering data, which are shown to be dependent upon a single function, though not the usual one. They then prove the continuity of the direct and inverse scattering transforms defined by the improved series for small complex potentials.Keywords
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