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We consider the large time asymptotic behavior of solutions to the Cauchyproblem for a dispersive-dissipative equation with a cubic nonlinearity. Byanalyzing the corresponding integral equation, the higher-order asymptoticexpansion for the solutions to the linear part and the first asymptotic profilefor the Duhamel term of the integral equation have been obtained. In thispaper, we construct the second asymptotic profile for the Duhamel term and givethe more detailed higher-order asymptotic expansion of the solutions, whichgeneralizes the previous works.

Higher-order asymptotic profiles for solutions to the Cauchy problem for a dispersive-dissipative equation with a cubic nonlinearity