The e^+e^- -> 3(\pi^+\pi^-), 2(\pi^+\pi^-\pi^0) and K^+K^-2(\pi^+\pi^-) Cross Sections at Center-of-Mass Energies 0.5--4.5 GeV Measured with Initial-State Radiation

We study the processes e{sup +}e{sup -} {yields} 3({pi}{sup +}{pi}{sup -}){gamma}, 2({pi}{sup +}{pi}{sup -}{pi}{sup 0}){gamma} and K{sup +}K{sup -} 2({pi}{sup +} {sup -}){gamma}, with the photon radiated from the initial state. About 20,000, 33,000 and 4,000 fully reconstructed events, respectively, have been selected from 232 fb{sup -1} of BABAR data. The invariant mass of the hadronic final state defines the effective e{sup +}e{sup -} center-of-mass energy, so that these data can be compared with the corresponding direct e{sup +}e{sup -} measurements. From the 3({pi}{sup +}{pi}{sup -}), 2({pi}{sup +}{pi}{sup -}{pi}{sup 0}) and K{sup +}K{sup -} 2({pi}{sup +}{pi}{sup -}) mass spectra, the cross sections for the processes e{sup +}e{sup -} {yields} 3({pi}{sup +}{sup -}), e{sup +}e{sup -} {yields} 2({pi}{sup +}{pi}{sup -}{pi}{sup 0}) and e{sup +}e{sup -} {yields} K{sup +}K{sup -} 2({pi}{sup +}{pi}{sup -}) are measured for center-of-mass energies from production threshold to 4.5 GeV. The uncertainty in the cross section measurement is typically 6-15%. We observe the J/{psi} in all these final states and measure the corresponding branching fractions