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Using a transport model coupled with a phase-space coalescence after-burnerwe study the triton-$^3$He ratio, relative and differential transverse flows insemi-central $^{132}Sn+^{124}Sn$ reactions at a beam energy of 400 MeV/A. Theneutron-proton ratio, relative and differential flows are also discussed as areference. We find that similar to the neutron-proton pairs the triton-$^3$Hepairs also carry interesting information about the density dependence of thenuclear symmetry energy. Moreover, the nuclear symmetry energy affects morestrongly the t-$^3$He relative and differential flows than the $\pi^-/\pi^+$ratio in the same reaction. The t-$^3$He relative flow can be used as aparticularly powerful probe of the high-density behavior of the nuclearsymmetry energy.

Triton-$^3$He relative and differential flows as probes of the nuclear symmetry energy at supra-saturation densities