Shamailov SSBrand J2023-11-292024-07-252023-11-292024-07-252018-03-01Shamailov SS, Brand J. (2018). Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves. SciPost Physics. 4. 3.2542-4653https://mro.massey.ac.nz/handle/10179/70431Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.(c) The Author/s 2018CC BY 4.0https://creativecommons.org/licenses/by/4.0/Journal article10.21468/SciPostPhys.4.3.0182542-4653journal-articlehttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000432739600005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=c5bb3b2499afac691c2e3c1a83ef6fefARTN 018