Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Long-lived localized field configurations such as breathers, oscillons, or more complex objects naturally arise in the context of a wide range of nonlinear models in different numbers of spatial dimensions. We present a numerical method, which we call the adiabatic damping method, designed to study such configurations in small lattices. Using three-dimensional oscillons in φ4 models as an example, we show that the method accurately (to one part in 105 or better) reproduces results obtained with static or dynamically expanding lattices, dramatically cutting down in integration time. We further present results for two-dimensional oscillons, whose lifetimes would be prohibitively long to study with conventional methods.
Gleiser, M. and Sornborger, A., "Long-Lived Localized Field Configurations in Small Lattices: Application to Oscillons" (1999). Open Dartmouth: Faculty Open Access Articles. 2895.