A kind of explicit Riemann theta functions periodic waves solutions for discrete soliton equations |
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| Institution: | 1. Max-Planck-Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany;2. Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany;3. Department of Mathematical Physics, Toyama Prefectural University, Kurokawa 5180, Imizu, Toyama, 939-0398, Japan |
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| Abstract: | In this paper, Riemann theta functions are used to construct one-theta function and two-theta functions solutions to a class of Hirota bilinear equations, such as extended version of the discrete mKdV equation and deautonomization of the two-dimensional Toda lattice equation. To get the Riemann theta function periodic waves solutions (the quasi-periodic solutions), this method is direct and simple which use only the identities of the theta functions. |
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