Using a symbolic computation for nontrivial equations is always a challenge. Examples are always helpful to others trying to use symbolic analysis. The authors report on their efforts to use Maple, one of the more capable programs, on bifurcation phenomena. The equations involved are systems of partial differential equations that are not overly messy, with solutions involving functions that are products of rational functions and exponentials, also not overly messy.

While the paper is well written, the equations and derivations are clearly presented, and the accompanying graphics are good, the paper is deficient in its symbolic aspects. The authors mention various Maple routines they developed, but provide neither details of functional forms used nor pseudocode for the implementation. One section does discuss methods used to perform symbolic manipulations, but does not exhibit any Maple formalisms. A 24-page report describing the use of Maple without a single line of Maple code is incomplete. The authors do not mention whether their Maple code is available, nor do they provide an Internet address where they can be contacted.

The paper is a good physics paper, and it describes MAPLE code that is probably useful. Unfortunately, it does not provide much advice or specific examples to help others apply Maple to complicated mathematical problems.