This monograph deals with Burgers' equation and its
generalisations. Such equations describe a wide variety of
nonlinear diffusive phenomena, for instance, in nonlinear
acoustics, laser physics, plasmas and atmospheric physics. The
Burgers equation also has mathematical interest as a canonical
nonlinear parabolic differential equation that can be exactly
linearised. It is closely related to equations that display soliton
behaviour and its study has helped elucidate other such nonlinear
behaviour. The approach adopted here is applied mathematical. The
author discusses fully the mathematical properties of standard
nonlinear diffusion equations, and contrasts them with those of
Burgers' equation. Of particular mathematical interest is the
treatment of self-similar solutions as intermediate asymptotics for
a large class of initial value problems whose solutions evolve into
self-similar forms. This is achieved both analytically and
numerically.
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