Fig. 7.

Comparison between numerical solution of Eq. (15) and long-wave solutions for (a) $\beta =1$, $\tau =1.25$, $\gamma =0.1$, $p=0.98$, $a=1\times 10^{-5}$ (DDE), and $P\left(0\right)=0.55\times 10^{-4}$ (long-wave); (b) Phase portrait of the long wave Eq. (62), the red thick line is the solution of Eq. (15).