Springer Waves in Continuous Media (Lecture Notes in Geosystems Mathematics and Computing)

Product Description 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. Review “This book is a graduate level text based upon a lecture course on waves in continuous media with particular emphasis on fluid media. It is aimed at students of applied mathematics, mechanics and geophysics. … Waves in a stratified fluid and stability of such waves are also discussed. A number of instructive examples and exercises are given that may be useful for the targeted audience.” (Fiazud Din Zaman, zbMATH 1364.76003, 2017) From the Back Cover 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. About the Author Sergey Gavrilyuk is professor at the Aix-Marseille III University, Marseille, France Nikolai MAKARENKO is professor at the Lavrentyev Institute of Hydrodynamics Siberian Branch of the Russian Academy, Novosibirsk, Russia Sergey SUKHININ is professor at the Lavrentyev Institute of Hydrodynamics Russian Academy of Sciences, Novosibirsk, Russia