Numerical investigation on the 3-periodic wave solutions of (1+1)-dimensional and (2+1)-dimensional integrable equations

Yutao Gong, Yunhu Wang and Huanhe Dong

Chaos, Solitons & Fractals, 2025, vol. 199, issue P1

Abstract: The direct method proposed by Akira Nakamura for finding N-periodic wave solutions yields quick results for N=1 and 2. However, when N≥3, the difficulty in solving over-determined systems makes it challenging to further obtain the periodic solutions of the equations. This paper combines the Gauss–Newton method with Akira Nakamura’s direct method to calculate 3-periodic wave solutions to four (1+1)-dimensional and (2+1)-dimensional integrable equations: the combined KdV–Caudrey–Dodd–Gibbon equation, the (2+1)-dimensional KdV equation, the (2+1)-dimensional Ito equation and the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation. Detailed numerical experiments are conducted to demonstrate the existence of 3-periodic wave solutions.

Keywords: Three-periodic wave solutions; Riemann theta function; Gauss–Newton method (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925006228
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006228

DOI: 10.1016/j.chaos.2025.116609

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().