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finally, since they lauched this I was waiting for someone to post it here
another batman function is found as a stationary solution of the non-linear 4th order extended Fisher-Kolmogorov equation:

u_t + 10^-8 u_xxxx = 10e^-4 gamma u_xx + u - u^3

which describes the propagation of domain walls in liquid crystals

batman-ears: http://www.matmol.org/images/images/kolmo.png