Thermal decay of planar Jones-Roberts solitons

Homogeneous planar superfluids exhibit a range of low-energy excitations that also appear in highly excited states like superfluid turbulence. In dilute gas Bose-Einstein condensates, the Jones-Roberts soliton family includes vortex dipoles and rarefaction pulses in the low- and high-velocity regimes, respectively. These excitations carry both energy and linear momentum, making their decay characteristics crucial for understanding superfluid dynamics. In this work, we develop the theory of planar soliton decay due to thermal effects, as described by the stochastic projected Gross--Pitaevskii theory of reservoir interactions. We analyze two distinct damping terms involving transfer between the condensate and the noncondensate reservoir: particle transfer that also involves energy and usually drives condensate growth, and number-conserving energy transfer. We provide analytical treatments for both the low- and high-velocity regimes and identify conditions under which either mechanism dominates. Our findings indicate that energy damping prevails at high phase-space density. These theoretical results are supported by numerical studies covering the entire velocity range from vortex dipole to rarefaction pulse. We use interaction energy to characterize rarefaction pulses, analogous to the distance between vortices in vortex dipoles, offering an experimentally accessible test for finite-temperature theory in Bose-Einstein condensates.