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This unique book aims to treat a class of nonlinear waves that are
reflected from the boundaries of media of finite extent. It
involves both standing (unforced) waves and resonant oscillations
due to external periodic forcing. The waves are both hyperbolic and
dispersive. To achieve this aim, the book develops the necessary
understanding of linear waves and the mathematical techniques of
nonlinear waves before dealing with nonlinear waves in bounded
media. The examples used come mainly from gas dynamics, water waves
and viscoelastic waves.
These lecture notes provide a fresh approach to investigating
singularly perturbed systems using asymptotic and geometrical
techniques. It gives many examples and step-by-step techniques,
which will help beginners move to a more advanced level. Singularly
perturbed systems appear naturally in the modelling of many
processes that are characterized by slow and fast motions
simultaneously, for example, in fluid dynamics and nonlinear
mechanics. This book's approach consists in separating out the slow
motions of the system under investigation. The result is a reduced
differential system of lesser order. However, it inherits the
essential elements of the qualitative behaviour of the original
system. Singular Perturbations differs from other literature on the
subject due to its methods and wide range of applications. It is a
valuable reference for specialists in the areas of applied
mathematics, engineering, physics, biology, as well as advanced
undergraduates for the earlier parts of the book, and graduate
students for the later chapters.
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