The fundamental characteristics of soliton and chaos in nonlinear equation are completely different. But all nonlinear equations with a soliton solution may derive chaos. While only some equations with a chaos solution have a soliton. The conditions of the two solutions are different. When some parameters are certain constants, the soliton is derived; while these parameters vary in a certain region, the bifurcation-chaos appears. It connects a chaotic control probably. Some possible meanings on the double solutions are discussed in mathematics, physics, particle theory and neurobiology. We propose a new type of soliton equation, whose solutions may describe some statistical distributions, for example, Cauchy distribution, normal distribution and student’s t distribution, etc. 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.