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.
