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A proper version of the proto renormalization-group scheme is presented toderive amplitude equations in striped pattern formation with conserved andnonconserved order parameter. In the conserved case, the result preserves theconservation law as well as the rotational invariance of the physical system.This makes a great contrast with existing singular perturbation theories suchas the multiple-scales method, in which the perturbation expansion truncated atany finite order destroys those symmetries.

Renormalization-group for amplitude equations in cellular pattern formation with and without conservation law