We show using numerical simulations that a variety of localized patterns arise in a model equation: the quintic Swift-Hohenberg equation with complex coefficients. We demonstrate that various sizes of localized standing wave patterns are possible when the imaginary part of the complex coefficient is small. Localized traveling waves as well as localized standing waves with a fixed size are observed when the imaginary part is rather large. We also present stable localized patterns in two spatial dimensions and study their interaction.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics