The present study examines weakly dissipative, weakly nonlinear waves in which the fundamental derivative changes sign. The undisturbed state is taken to be at rest, uniform and in the vicinity of the 0 locus. The cubic Burgers equation governing these waves is solved numerically; the resultant solutions are compared and contrasted to those of the invisced theory. Further results include the presentation of a natural scaling law and inviscid solutions not reported elsewhere
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