High energy density in the collision of $N$ kinks in the $\phi^4$ model
  Recently for the sine-Gordon equation it has been established that during collisions of $N$ slow kinks maximal energy density increases as $N^2$. In this numerical study, the same scaling rule is established for the non-integrable $\phi^4$ model for $N\le 5$. For odd (even) $N$ the maximal energy density is in the form of potential (kinetic) energy density. Maximal elastic strain is also calculated. In addition, the effect of the kink's internal modes on the maximal energy density is analysed for $N=1, 2, 3$. Our results suggest that in multi-soliton collisions very high energy density can be achieved in a controllable manner. 
Aliakbar M. Marjaneh, Danial Saadatmand, Kun Zhou, Sergey V. Dmitriev,   Mohammad E. Zomorrodian
nlin.PS