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Abstract
Based on the system of equations for the Bose–Einstein condensate to the third order in the interaction radius, a nonlinear integro-differential equation of the third order, whose particular case is the Korteweg–de Vries equation to the first order in the interaction radius, is obtained. The profile of nonlinear stationary perturbations of boson concentration in a system with short-range interaction potential is found and investigated, and the corresponding expression for the wave function in the medium is obtained.
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