A Klein-Gordon model with cubic and logarithmic interactions supports self-trapped quantum droplet solutions whose non-relativistic limit yields a generalized Gross-Pitaevskii equation with logarithmic correction.
One-dimensional klein–gordon equation with logarithmic nonlinearities.Journal of Physics A: Mathematical and Theoretical, 41(35):355201
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Emergent Quantum Droplets in Logarithmic Klein-Gordon Models of Bose-Einstein Condensates
A Klein-Gordon model with cubic and logarithmic interactions supports self-trapped quantum droplet solutions whose non-relativistic limit yields a generalized Gross-Pitaevskii equation with logarithmic correction.