  In multiple-front solutions of the Burgers equation, all the fronts, except
for two, are generated through the inelastic interaction of exponential wave
solutions of the Lax pair associated with the equation. The inelastically
generated fronts are the source of two difficulties encountered in the standard
Normal Form expansion of the approximate solution of the perturbed Burgers
equation, when the zero-order term is a multiple-front solution: (i) The
higher-order terms in the expansion are not bounded; (ii) The Normal Form
(equation obeyed by the zero-order approximation) is not asymptotically
integrable; its solutions lose the simple wave structure of the solutions of
the un-perturbed equation. The freedom inherent in the Normal Form method
allows a simple modification of the expansion procedure, making it possible to
overcome both problems in more than one way. The loss of asymptotic
integrability is shifted from the Normal Form to the higher-order terms (part
of which has to be computed numerically) in the expansion of the solution. The
front-velocity update is different from the one obtained in the standard
analysis.
