Long-lived localized field configurations in small lattices: Application to oscillons

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 ${\phi }^4$ models as an example, we show that the method accurately (to one part in ${10}^5$ 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.