Asymptotic, as $t\to\infty$, of the solution of a nonlinear equation with weak dissipation and dispersion

The asymptotics as $t\to\infty$, uniformly with respect to $x\in R_1$, is found for a solution of a model nonlinear nonlocal evolution equation in the case of weak dissipation and dispersion. The leading term of the asymptotics has the same form as for the linearized equation.