Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System |
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Authors: | Fengfeng Dong Lingjun Zhou |
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Affiliation: | 1. School of Mathematical Sciences, Tongji University, Shanghai 200092, P.R. China;2. School of Mathematical Sciences, Tongji University, Shanghai 200092, P.R. China, zhoulj@tongji.edu.cn |
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Abstract: | In this paper, we are concerned with the explicit construction of peakon solutions of the integrable twocomponent system with cubic non-linearity. We establish the spectral and inverse spectral problem associated to the Lax pairs of the system. The inverse problem is solved by the classical results of Stieltjes continued fractions, which also contributes a lot to the spectral problem. The explicit formulas are obtained from solutions of the inverse problem. The positivity of the spectral measures is implied by J. Moser's work on the Jacobi spectral problem. |
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Keywords: | peakon two-component Camassa-Holm system continued fractions inverse spectral approach |
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