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Method of finding analytical solutions to some nonlinear differential equations of dissipative critical dynamics.

In this paper we develop a method of finding analytical solutions to the class of nonlinear ordinary differential equations given by f«+A (f)f'+B(f)f' 2 +C(f)=0. These types of equations appear frequently in mathematical physics and its applications to the kinetics of dissipative critical systems. Except for very special cases, little is known about their analytical solutions. Following a presentation of the method and its results, several particular examples are investigated in some detail