Nonlinear steady-state traveling solutions of the Kuramoto-Sivashinsky equation coupled with the linear dissipative equation

Andrey A. Bocharov and Oleg Yu. Tsvelodub

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: A generalization of the known active-dissipative Kuramoto-Sivashinsky equation coupled with a linear dissipative equation is considered. In such a model the region of zero solution instability is shown to depend in a complex way on the specific values of the problem parameters. The families of periodic nonlinear steady-state traveling solutions bifurcating from the zero solution in the vicinity of neutral wave numbers are constructed numerically. The investigation of the stability of these solutions enables obtaining new families that appear as a result of subsequent bifurcations. Among these families the ones that extend into the region of small wave numbers and turn into soliton solutions in the limit by the wave numbers are found among them. Various two-hump solitons are constructed. The research results on the stability of a soliton solution are presented.

Keywords: Coupled Kuramoto–Sivashinsky equation; Non-linear waves; Solitons; Stability; Bifurcation (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925005855
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:198:y:2025:i:c:s0960077925005855

DOI: 10.1016/j.chaos.2025.116572

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. ().