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We proposed a new type of soliton equation, whose solutions may describe somestatistical distributions, for example, Cauchy distribution, normaldistribution and student distribution, etc. The equation possesses twocharacters. Further, from an extension of this type of equation we may obtainthe exponential distribution, and the Fermi-Dirac distribution in quantumstatistics. Moreover, by using the method of the soliton-solution, thenonlinear Klein-Gordon equation and nonlinear Dirac equations may deriveBose-Einstein and Fermi-Dirac distributions, respectively, and bothdistributions may be unified by the nonlinear equation.

New Type of Soliton Equation Described Some Statistical Distributions and Nonlinear Equations Unified Quantum Statistics