High energy density in the collision of N kinks in the ϕ4 model

Abstract

Recently for the sine-Gordon equation it has been established that during collisions of N slow kinks maximal energy density increases as N2. In this numerical study, the same scaling rule is established for the non-integrable ϕ4 model for N ≤ 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, and 3. Our results suggest that in multi-soliton collisions very high energy density can be achieved in a controllable manner.