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We study a (1+1)-dimensional field theory based on $(\psi \ln \psi)^2$potential. There are three degenerate minima at $\psi = 0$ and $\psi=\pm1$.There are novel, asymmetric kink solutions of the form $\psi = \mp\exp(-\exp(\pm x))$ connecting the minima at $\psi = 0$ and $\psi = \mp 1$. Thedomains with $\psi = 0$ repel the linear excitations, the waves (e.g. phonons).Topology restricts the domain sequences and therefore the ordering of thedomain walls. Collisions between domain walls are rich for properties such astransmission of kinks and particle conversion, etc. To our knowledge this isthe first example of kinks with super-exponential profiles andsuper-exponential tails. Finally, we provide a comparison of these results withthe $\phi^6$ model and its half-kink solution.

A model field theory with $(\psi \ln \psi)^2$ potential: Kinks with super-exponential profiles