https://doi.org/10.1140/epjp/s13360-026-07390-5
Regular Article
Effects of nonlinear gradient terms in two-dimensional subcritical systems
1
Department of base scientists education, Advanced Teacher’s Training College for Technical Education, P.O.Box 8213, Douala, Cameroun
2
Department of Physics, Faculty of science, Pure Physics Laboratory, Group of Nonlinear Physics and Complex Systems, P.O.Box 24157, Douala, Cameroon
3
Applied Mechanics laboratory, Faculty of Sciences, P.O Box 812, Yaoundé I, Cameroun
a
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Received:
30
September
2025
Accepted:
1
February
2026
Published online:
21
February
2026
Abstract
Nonlinear gradient terms are known to stabilize dynamics in one-dimensional dissipative systems. This work extends their study to the two-dimensional (2D) cubic–quintic complex Ginzburg–Landau equation (CQGLE). It reveals a rich variety of spatiotemporal behaviors observed in many fields including biology, engineering, physics, and so on. By considering a turbulence defect regime, we find that the addition of nonlinear gradient terms can profoundly alter the system’s behavior. Indeed, the initially unstable system becomes stable due to these terms. Their presence can progressively suppress spatiotemporal chaotic regime, giving rise to new dynamical states such as weak-turbulence and laminar regime. Thus, in the two-dimensional subcritical Ginzburg–Landau equation, nonlinear gradient terms can be considered as a stabilizing mechanism.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
