Showing nlin.PSShow all
3 papers · 1 filter
nlin.PS2026
Global bifurcation of localised 2D patterns emerging from spatial heterogeneity
Dan J. Hill, David J. B. Lloyd, Matthew R. Turner
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations contai…
nlin.PS2025
Localized Patterns
Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-under…
nlin.PS2025
Numerical Continuation and Bifurcation in Nonlinear PDEs: Stability, invasion and wavetrains in the Swift-Hohenberg equation
David Lloyd, Ryan Goh, Jens D. M. Rademacher
We discuss some aspects of numerical continuation and bifurcation for partial differential equations, specifically pattern formation and coherent structures. For the sake of clarit…