Soliton and traveling-wave solutions in coupled one-dimensional condensates

Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports various density and phase solitons. Many theories of the 1D Bose gas rely on mean-field or quasiparticle frameworks, which may suffer from infrared singularities, often causing the small-fluctuation expansion to lose validity in long-wavelength regimes. Thus, we explore the physics using the bosonization technique as a complement in the long-wavelength regime, in which the phase and density are conjugate pairs, and determine its effective Language equation and the associated equation of motion. We show that in the presence of asymmetry between the two condensates, alternative solutions beyond those in the sine-Gordon model emerge. We calculate the traveling-wave solutions and soliton solutions in this model and determine their corresponding energy densities analytically. Finally, we discuss the relevance of these solutions to the experiments and discuss their observations. Since the physical models have already been realized in experiments, this work opens alternative possibilities for the realization of various soliton and periodic solutions using two coupled condensates.