We study relaxation dynamics of dark soliton, created by a phase-imprinted method, in a two-dimensional trapped Bose–Einstein condensate at nonzero temperatures by using the projected Gross–Pitaevskii equation. At absolute zero temperature, a dark soliton is known to decay with a snake instability. At nonzero temperature, as expected, we find that this snake instability cannot be seen as clearly as in the absolute zero temperature case because of the presence of thermal fluctuations. We find that the energy dependence of the decay rate, defined by the half-life of the fidelity with respect to the phase-imprinted initial state, shows a power law decay and approaches a nonzero value in the large energy limit.
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