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On the 100th anniversary of the birth of V.L. Ginzburg. Methodological notes
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Dynamics of solitary waves in ultracold gases in terms of observable quantities
L.P. Pitaevskii a, b
a Kapitza Institute of Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 117334, Russian Federation
b Dipartimento di Fisica, Università di Trento and BDC Center, Povo, Trento, I-38050, Italy
In recent years different solitary waves, like solitons, vortex rings, solitonic vortices, and more complicated, were
predicted. They can move in superfluid ultracold gases along elongated traps. A theoretical description of the moving
demands knowledge of two functions, the inertial mass of the soliton and the effective number of particles. They can
be calculated on the basis of a microscopic theory. However, one can express them in the the terms of observable
quantities - the phase increment and the depletion of number of particles in soliton. In this note a transparent
derivation of the corresponding equations is suggested. The results are applied to the "magnetic soliton" in mixtures
of Bose-gases in different spin states,which was predicted recently.
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