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The algebro-geometric solutions for the modified Camassa-Holm hierarchy

This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the modified Camassa-Holm (MCH) hierarchy through %and studying a algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism to derive the MCH hierarchy, the hyperelliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. With the help of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire MCH hierarchy.

preprint2012arXivOpen access
Yu HouEngui FanZhijun Qiao
nlin.SI
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Open access3 authors1 topic
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Yu HouEngui FanZhijun Qiao

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