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The dynamics of pions and strange particles in heavy-ion collisions in theregion of 1A GeV energies is investigated by the lanzhou quantum moleculardynamics model for probing the nuclear equation of state at supra-saturationdensities. The total multiplicities and the ratios obtained in$^{197}$Au+$^{197}$Au over $^{12}$C+$^{12}$C systems are calculated forselected Skyrme parameters SkP, SLy6, Ska and SIII, which correspond todifferent modulus of incompressibility of symmetric nuclear matter anddifferent cases of the stiffness of symmetry energy. A decrease trend of theexcitation functions of the ratios for strange particle production withincreasing incident energy was observed. The available data of K$^{+}$production measured by KaoS collaboration are described well with the parameterSkP, which results in a soft equation of state. The conclusions can not bemodified by an in-medium kaon-nucleon potential.

Constraining the high-density behavior of nuclear equation of state from strangeness production in heavy-ion collisions