We study the processes e+e−→γISRJ/ψ, where J/ψ→π+π−π0, J/ψ→K+K−π0, and J/ψ→K0SK±π∓ using a data sample of 519 fb−1 recorded with the BABAR detector operating at the SLAC PEP-II asymmetric-energy e+e− collider at center-of-mass energies at and near the Υ(nS) (n=2,3,4) resonances. We measure the ratio of branching fractions R1=B(J/ψ→K+K−π0)B(J/ψ→π+π−π0) and R2=B(J/ψ→K0SK±π∓)B(J/ψ→π+π−π0). We perform Dalitz plot analyses of the three J/ψ decay modes and measure fractions for resonances contributing to the decays. We also analyze the J/ψ→π+π−π0 decay using the Veneziano model. We observe structures compatible with the presence of ρ(1450) in all three J/ψ decay modes and measure the relative branching fraction: R(ρ(1450))=B(ρ(1450)→K+K−)B(ρ(1450)→π+π−)=0.307±0.084(stat)±0.082(sys).
