2007 年 76 巻 12 号 p. 124004
Based on the Riemann theta function, the Hirota bilinear method is extended to directly construct periodic wave solutions of KdV–Sawada–Kotera equation. The relations among various data related to the Riemann theta functions are explicitly given by the Fourier series representation. The asymptotic property of the periodic wave solution of the KdV–Sawada–Kotera equation is analyzed in detail. It is shown that well-known soliton solution given by Hirota can be reduced from the periodic wave solution.
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