Abstract
The sine-Gordon model captures the low-energy effective dynamics of a wealth of one-dimensional quantum systems, stimulating the experimental efforts in building a versatile quantum simulator of this field theory and fueling the parallel development of new theoretical toolkits able to capture far-from-equilibrium settings. In this work, we analyze the realization of sine-Gordon from the interference pattern of two one-dimensional quasicondensates: we argue the emergent field theory is well described by its classical limit and develop its large-scale description based on Generalized Hydrodynamics. We show how, despite sine-Gordon being an integrable field theory, trap-induced inhomogeneities cause instabilities of excitations and provide exact analytical results to capture this effect.