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• W2088661708 endingPage "1384" @default.
• W2088661708 startingPage "1348" @default.
• W2088661708 abstract "Based on two sets of the Lenard recursion gradients, we derive the three-wave resonant interaction (TWRI) hierarchy associated with a $3times 3$ matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the TWRI hierarchy, we introduce a trigonal curve ${cal K}_{m-2}$ of arithmetic genus $m-2$ with three infinite points and establish the corresponding Baker--Akhiezer function and meromorphic functions on ${cal K}_{m-2}$. The TWRI equations are decomposed into a system of Dubrovin-type ordinary differential equations. Using the theory of the trigonal curve and the properties of the three kinds of Abel differentials, we obtain the explicit theta function representations of the Baker--Akhiezer function, of the meromorphic functions, and, in particular, of solutions for the entire TWRI hierarchy." @default.
• W2088661708 created "2016-06-24" @default.
• W2088661708 creator A5021432692 @default.
• W2088661708 creator A5031706589 @default.
• W2088661708 creator A5066890510 @default.
• W2088661708 date "2014-01-01" @default.
• W2088661708 modified "2023-09-23" @default.
• W2088661708 title "Algebro-geometric Quasi-periodic Solutions to the Three-Wave Resonant Interaction Hierarchy" @default.
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• W2088661708 doi "https://doi.org/10.1137/130918794" @default.
• W2088661708 hasPublicationYear "2014" @default.
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