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A potential including Heaviside function in 1+1 dimensional hydrodynamics by Landau

In 1+1 dimensional hydrodynamics originally proposed by Landau, we derive a new potential and distribution function including Heaviside function and investigate its mathematical and physical properties. Using the original distribution derived by Landau, a distribution function found by Srivastava et al., our distribution function, and the Gaussian distribution proposed by Carruthers et al., we analyze the data of the rapidity distribution on charged pions and K mesons at RHIC energies (sqrt(s_NN) = 62.4 GeV and 200 GeV). Three distributions derived from the hydrodynamics show almost the same chi-squared values provided the CERN MINUIT is used. We know that our calculations of hadron's distribution do not strongly depend on the range of integration of fluid rapidity, contrary to that of Srivastava et al. Finally the roles of the Heaviside function in concrete analyses of data are investigated.