With the help of the method of similarity transformations, an approach is considered that makes it possible to find particular solutions of the Gross–Pitaevskii equation with a nonstationary coefficient of nonlinearity in prolate spheroidal coordinates. Two exact solutions are found in explicit form, having soliton properties, along with the corresponding potentials. The form of the solutions is illustrated by examples.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 2014.
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Borisov, A.V., Shapovalov, A.V. Solutions of the Gross–Pitaevskii Equation in Prolate Spheroidal Coordinates. Russ Phys J 57, 1201–1209 (2015). https://doi.org/10.1007/s11182-015-0364-5
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DOI: https://doi.org/10.1007/s11182-015-0364-5