The direct method of calculating the multi-periodic wave solutions by Nakamura are applied to the following equations; the Korteweg-de Vrics equation, the Toda equation, the Sawada-Kotera equation and the model equation for shallow water waves, and are obtained three-periodic wave solutions expressed in terms of Riemann's θ-function. All parameters determining the characters of the wave are obtained numerically.
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Hirota et al. (1981) studied this question.
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