In this paper, based on the direct method proposed by Akira Nakamura, we present an efficient numerical scheme to calculate the N-periodic wave solutions to the Tzitzeica equation and the (2 + 1)-dimensional modified Bogoyavlenskii-Schiff (mBS) equation which can be transformed into a coupled bilinear system with some dependent variable transformation. By using this numerical scheme, we calculate their 2-periodic wave solutions and 3-periodic wave solutions as examples. We also show the asymptotic behaviors under a “small amplitude” limit of these quasi-periodic wave solutions numerically.

中文翻译：

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两个耦合双线性方程组N周期波解的数值研究

本文基于中村明（Akira Nakamura）提出的直接方法，提出了一种有效的数值方案，用于计算Tzitzeica方程和（2 +1）维修正的Bogoyavlenskii-Schiff（mBS）方程的N周期波解，可以将其转换为具有一些因变量转换的耦合双线性系统。通过使用此数值方案，我们以它们的2周期波动解和3周期波动解为例进行计算。我们还显示了在这些准周期波解的“小幅度”极限下的渐近行为。