A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation |
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| Authors: | Xianguo Geng Bo Xue Jiao Wei |
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| Institution: | 1. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001, People’s Republic of China, xggeng@zzu.edu.cn (Xianguo Geng);2. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001, People’s Republic of China, xuebo@zzu.edu.cn (Bo Xue);3. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001, People’s Republic of China, weijiaozzu@163.com (Jiao Wei) |
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| Abstract: | Based on the Lenard recursion relation and the zero-curvature equation, we derive a hierarchy of long wave-short wave type equations associated with the 3 × 3 matrix spectral problem with three potentials. Resorting to the characteristic polynomial of the Lax matrix, a trigonal curve is defined, on which the Baker-Akhiezer function and two meromorphic functions are introduced. Analyzing some properties of the meromorphic functions, including asymptotic expansions at infinite points, we obtain the essential singularities and divisor of the Baker-Akhiezer function. Utilizing the theory of algebraic curves, quasi-periodic solutions for the entire hierarchy are finally derived in terms of the Riemann theta function. |
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| Keywords: | long wave-short wave type equations Baker-Akhiezer function meromorphic function quasiperiodic solutions |
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