Geodesic
Asymptotic, as $t\to\infty$, of the solution of a nonlinear equation with weak dissipation and dispersion
Izvestiya. Mathematics , Tome 43 (1994) no. 3, pp. 443-453

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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. 
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     author = {P. I. Naumkin and I. A. Shishmarev},
     title = {Asymptotic, as $t\to\infty$, of the solution of a nonlinear equation with weak dissipation and dispersion},
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P. I. Naumkin; I. A. Shishmarev. Asymptotic, as $t\to\infty$, of the solution of a nonlinear equation with weak dissipation and dispersion. Izvestiya. Mathematics , Tome 43 (1994) no. 3, pp. 443-453. http://geodesic.mathdoc.fr/item/IM2_1994_43_3_a2/