Zhang Yingnan, Hu Xingbiao, Sun Jianqing
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People's Republic of China.
LSEC, Institute of Computational Mathematics and Scientific Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, People's Republic of China.
Proc Math Phys Eng Sci. 2021 Jan;477(2245):20200752. doi: 10.1098/rspa.2020.0752. Epub 2021 Jan 13.
In this paper, we study the -periodic wave solutions of coupled Korteweg-de Vries (KdV)-Toda-type equations. We present a numerical process to calculate the -periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of = 3, we give some detailed examples to show the -periodic wave solutions to the coupled Ramani equation, the Hirota-Satsuma coupled KdV equation, the coupled Ito equation, the Blaszak-Marciniak lattice, the semi-discrete KdV equation, the Leznov lattice and a relativistic Toda lattice.
在本文中，我们研究了耦合的科特韦格 - 德弗里斯（KdV） - 托达型方程的 - 周期波解。我们基于中村晃提出的计算周期波解的直接方法，给出了一个计算 - 周期波的数值过程。特别地，在 = 3 的情况下，我们给出了一些详细的例子来展示耦合拉马尼方程、广田 - 萨摩耦合KdV方程、耦合伊藤方程、布拉斯扎克 - 马尔齐尼亚克晶格、半离散KdV方程、列兹诺夫晶格和相对论托达晶格的 - 周期波解。
