Large time behavior of solutions to the Cauchy problem for the BBM–Burgers equation

We consider the large time behavior of solutions to Cauchy problem for BBM-Burgers equation. prove that solution this goes self-similar Burgers equation called nonlinear diffusion wave. Moreover, we construct appropriate second asymptotic profiles depending on initial data. Based discussion, investigate effect data solution, and derive optimal rate Especially, important point study is with slowly decaying data, whose case has not been studied, are obtained.