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Hybrid Models of Step Bunching

We introduce two hybrid models of step bunching on vicinal crystal surfaces. The model equations for step velocity are constructed by the two possible exchanges of terms between the equations of two primary models MM2 and LW2 [arXiv:1011.1863], both showing the specific type of bunching with minimal step-step distance lmin in the bunch independent of the number of steps N in it. This feature is preserved only in the hybrid model LW2MM (the first term in the model equation comes from LW2 and the second one - from MM2) but in a rather complex fashion -- the surface slope is largest in the both ends of the bunch and after a sharp decrease jumps again to become constant in the inner part. We restrict our considerations to the simplest case of p = 0, p being the exponent in the destabilizing term in the velocity equations. The time-scaling exponent of N in LW2MM is ~1/3 and is independent of n, the exponent in the stabilizing term of the velocity equations. The other model, MM2LW, shows an interesting type of step bunching -- some bunches grow to a certain size and then decay emitting steps towards the two adjacent bunches. The bunch compression with the increase of N is pronounced.