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Swift-Hohenberg equation with broken cubic-quintic nonlinearity
1School of Mathematics, University of Leeds, Leeds, United Kingdom. smh@maths.leeds.ac.uk
Summary
Breaking midplane reflection symmetry in the Swift-Hohenberg equation (SH35) alters localized structures. This symmetry breaking leads to drifting convectons and structure collisions in convective systems.
Area of Science:
- Nonlinear dynamics
- Fluid mechanics
- Pattern formation
Background:
- The cubic-quintic Swift-Hohenberg equation (SH35) models convective systems with midplane reflection symmetry.
- Localized structures in these systems exhibit unique organizational patterns.
Purpose of the Study:
- To investigate the impact of breaking midplane reflection symmetry on localized structures.
- To analyze the generation of familiar structures and the behavior of convectons.
Main Methods:
- Utilized the SH35 equation with an added quadratic term to break symmetry.
- Studied the deformation of "snakes-and-ladders" organization.
- Analyzed the dynamics of odd-parity convectons in nonvariational systems.
Main Results:
- Symmetry breaking deforms the "snakes-and-ladders" organization.
- This deformation generates the structure seen in the quadratic-cubic Swift-Hohenberg equation.
- Broken symmetry induces drift in odd-parity convectons, enabling structure collisions.
Conclusions:
- Midplane reflection symmetry breaking significantly alters localized structure dynamics.
- Drifting convectons and their collisions are key consequences of symmetry breaking.
- The study provides insights into pattern formation in systems like binary fluid convection.
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