On the Inverse Spectral Problem for the Camassa–Holm Equation

✍ Scribed by Adrian Constantin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 306 KB
• Volume: 155
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3231

✦ Synopsis

A key basis for seeking periodic solutions of the Camassa Holm equation is to understand the associated spectral problem y$= 1 4 y+*my. The periodic spectrum can be recovered from the norming constants and the elements of the auxiliary spectrum. The potential can then be reconstructed from the periodic spectrum. A necessary and sufficient condition for exponential decrease of the widths * 2n &* 2n&1 for a sequence 0<* 1 * 2 < } } } of single or double eigenvalues tending to infinity is the real analyticity of m. The case of a purely simple spectrum is typical of 0>m # C 1 (R).