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Pattern formation in a Swift-Hohenberg equation with spatially periodic coefficients
Jolien Kamphuis, Martina Chirilus-Bruckner
https://arxiv.org/abs/2506.22211

Pattern formation in a Swift-Hohenberg equation with spatially periodic coefficients
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by solutions of a Ginzburg-Landau type equation. Since the interplay between forcing wavenumber and intrinsic wavenumber crucially shapes the spectrum and emerging patterns, we distinguish between resonant and non-resonant regimes. Extending earlier work that assumed …

Beating solitons with nonzero relative wavenumber, their interaction, and coexistence with Akhmediev breathers
Wen-Juan Che, Chong Liu
https://arxiv.org/abs/2506.16989

Beating solitons with nonzero relative wavenumber, their interaction, and coexistence with Akhmediev breathers
We study beating solitons and their interaction for the three-component nonlinear Schrödinger equations (NLSEs) in both focusing and defocusing cases. We identify a previously unknown family of beating solitons with nonzero relative wavenumber which is absent in the two-component NLSEs. Existence diagrams of these beating solitons are extracted from the exact solutions. Unique coexistence and interaction between beating solitons and vector Akhmediev breathers are revealed by using the existenc…

Synchronization of Dirac-Bianconi driven oscillators
Riccardo Muolo, Iv\'an Le\'on, Yuzuru Kato, Hiroya Nakao
https://arxiv.org/abs/2506.20163 http…

Synchronization of Dirac-Bianconi driven oscillators
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network theory addresses this by considering variables defined on nodes, links, triangles, and higher-order simplices, called topological signals (or cochains). Moreover, topological signals of different dimensions can interact through the Dirac-Bianconi operator, w…

Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation
Thomas Jun Jewell, Andrew L. Krause, Philip K. Maini, Eamonn A. Gaffney
https://arxiv.org/abs/2505.17372

Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation
Chase-and-run dynamics, in which one population pursues another that flees from it, are found throughout nature, from predator-prey interactions in ecosystems to the collective motion of cells during development. Intriguingly, in many of these systems, the movement is not straight; instead, 'runners' veer off at an angle from their pursuers. This angled movement often exhibits a consistent left-right asymmetry, known as lateralisation or chirality. Inspired by such phenomena in zebrafish skin p…

Modelling intermediate internal waves with currents and variable bottom
Rossen Ivanov, Lyudmila Ivanova
https://arxiv.org/abs/2506.10123 https://

Modelling intermediate internal waves with currents and variable bottom
A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet-Neumann operators for the two fluid domains, and the depth-dependent current is taken into accoun…