  We proposed a new type of soliton equation, whose solutions may describe some
statistical distributions, for example, Cauchy distribution, normal
distribution and student distribution, etc. The equation possesses two
characters. Further, from an extension of this type of equation we may obtain
the exponential distribution, and the Fermi-Dirac distribution in quantum
statistics. Moreover, by using the method of the soliton-solution, the
nonlinear Klein-Gordon equation and nonlinear Dirac equations may derive
Bose-Einstein and Fermi-Dirac distributions, respectively, and both
distributions may be unified by the nonlinear equation.
