  We show that low-angle grain boundaries (GB) in high-temperature
superconductors exhibit intermediate Abrikosov vortices with Josephson cores,
whose length $l$ along GB is smaller that the London penetration depth, but
larger than the coherence length. We found an exact solution for a periodic
vortex structure moving along GB in a magnetic field $H$ and calculated the
flux flow resistivity $R_F(H)$, and the nonlinear voltage-current
characteristics. The predicted $R_F(H)$ dependence describes well our
experimental data on $7^{\circ}$ unirradiated and irradiated $YBa_2Cu_3O_7$
bicrystals, from which the core size $l(T)$, and the intrinsic depairing
density $J_b(T)$ on nanoscales of few GB dislocations were measured for the
first time. The observed temperature dependence of $J_b(T)=J_{b0}(1-T/T_c)^2$
indicates a significant order parameter suppression in current channels between
GB dislocation cores.
