| Abstract: |
| With the aid of Lenard recursion equations, we derive the Lax pair of the coupled long wave-short wave resonance hierarchy, in which the first nontrivial member is the coupled long wave-short wave resonance equations. The properties of the associated Riemann surface are under consideration, especially including arithmetic genus and holomorphic differentials. By comparing the asymptotic expansions for the Baker-Akhiezer function and its Riemann theta function representation, we obtain Algebro-geometric solutions of the entire coupled long wave-short wave resonance hierarchy in terms of the Riemann theta function. |
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