Dynamics of nonself-similar solutions of the Dawson equation

We study the dynamics of nonself-similar solutions of the Cauchy problem for a stochastic partial differential Itô equation of the parabolic type with linear principal part and with the diffusion coefficient that is exponential function whose exponent is larger than zero, but is less than 1. The equations of such a type are named the Dawson equations. It is proved that the solution that is of a nonself-similar form and is generated by a finite initial function behaves itself in the course of time analogously to a self-similar solution.