In quasi-1D and quasi-2D dipolar Bose gases the soliton-to-droplet transition occurs either as a first-order phase transition with bistability or as a smooth crossover, with the breathing-mode response serving as an accessible experimental signature.
Rajaraman,Solitons and Instantons: An Introduc- tion to Solitons and Instantons in Quantum Field The- ory(North-Holland Publishing Company, Amsterdam, Netherlands, 1982)
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Soliton-to-droplet crossover in a dipolar Bose gas in one and two dimensions
In quasi-1D and quasi-2D dipolar Bose gases the soliton-to-droplet transition occurs either as a first-order phase transition with bistability or as a smooth crossover, with the breathing-mode response serving as an accessible experimental signature.