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Starting with the basic notions and facts of the mathematical
theory of waves illustrated by numerous examples, exercises, and
methods of solving typical problems Chapters 1 & 2 show e.g.
how to recognize the hyperbolicity property, find characteristics,
Riemann invariants and conservation laws for quasilinear systems of
equations, construct and analyze solutions with weak or strong
discontinuities, and how to investigate equations with dispersion
and to construct travelling wave solutions for models reducible to
nonlinear evolution equations. Chapter 3 deals with surface and
internal waves in an incompressible fluid. The efficiency of
mathematical methods is demonstrated on a hierarchy of approximate
submodels generated from the Euler equations of homogeneous and
non-homogeneous fluids. The self-contained presentations of the
material is complemented by 200+ problems of different level of
difficulty, numerous illustrations, and bibliographical
recommendations.
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