Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

Keivan Mohajer; Jacek Szmigielski

doi:10.1088/0266-5611/28/1/015002

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arXiv · 1107.1329

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

Keivan Mohajer·Jacek Szmigielski

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Abstract

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works.

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Keivan Mohajer, Jacek Szmigielski. 2011-07-07. Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I. https://doi.org/10.1088/0266-5611%2F28%2F1%2F015002

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