<p>The Korteweg – de Vries – Burgers equation, the modified Korteweg – de Vries – Burgers equation, the dissipative Gardner equation and the nonlinear differential equation for description surface waves in a convecting fluid are considered. The Cauchy problems for all these partial differential equations are not solved by theinverse scattering transform. Reductions of these equations to nonlinear ordinary differentialequations do not pass the Painlevé test. However, there are local expansions of the generalsolutions in the Laurent series near movable singular points.We demonstrate that the obtained information from the Painlevé test for reductions ofnonlinear evolution dissipative differential equations can be used to construct thenonautonomous first integrals of nonlinear ordinary differential equations. Taking intoaccount the found first integrals, we also obtain analytical solutions of nonlinear evolutiondissipative differential equations. Our approach is illustrated to obtain thenonautonomous first integrals for reduction of the Korteweg – de Vries – Burgers equation,the modified Korteweg – de Vries – Burgers equation, the dissipative Gardner equation andthe nonlinear differential equation for description surface waves in a convecting fluid.The obtained first integrals are used to construct exact solutions of the above-mentionednonlinear evolution equations with as many arbitrary constants as possible. It is shown thatsome exact solutions of the equation for description of nonlinear waves in a convectingliquid are expressed via the Painlevé transcendents.</p>