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Statics and dynamics of a binary dipolar Bose-Einstein condensate soliton

We study the statics and dynamics of a binary dipolar Bose-Einstein condensate soliton for repulsive inter- and intraspecies contact interactions with the two components subject to different spatial symmetries $-$ distinct quasi-one-dimensional and quasi-two-dimensional shapes - using numerical solution and variational approximation of a three-dimensional mean-field model. The results are illustrated with realistic values of parameters in the binary 164Dy-168Er mixture. The possibility of forming robust dipolar solitons of very large number of atoms make them of great experimental interest. The existence of the solitons is illustrated in terms of stability phase diagrams. Exotic shapes of these solitons are illustrated in isodensity plots. The variational results for statics (size and chemical potential) and dynamics (small oscillation) of the binary soliton compare well with the numerical results. A way of preparing and studying these solitons in laboratory is suggested.