Numerical calculation of N-periodic wave solutions to coupled KdV–Toda-type equations. (13th January 2021)

• Record Type: Journal Article
• Authors: Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing
• Is Part Of: Proceedings. Volume 477:Number 2245(2021)
• Publication Date: 2021-01-13
• Subjects: N-periodic wave solution -- coupled KdV–Toda-type equation -- Riemann's θ-function -- the direct method; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0752
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : In this paper, we study the N -periodic wave solutions of coupled Korteweg–de Vries (KdV)–Toda-type equations. We present a numerical process to calculate the N -periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of N = 3, we give some detailed examples to show the N -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.