EAN: 9783319206899

NEW APPROACHES TO NONLINEAR WAVES KARTONIERT (TB)

The book details a few of the novel methods developed in the last few years for studying
various aspects of nonlinear wave systems. The introductory chapter provides a general overview
thematically linking the objects described in the book. Two chapters are devoted to wave
systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear
frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of
equations is studied using rigorous mathematical methods (Chapter 4) and its possible
connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the
choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain
a deeper insight into the properties of a specific wave system. The final chapter discusses
problems encountered when attempting to verify the theoretical predictions using numerical or
laboratory experiments. All the chapters are illustrated by ample constructive examples
demonstrating the applicability of these novel methods and approaches to a wide class of
evolutionary dispersive PDEs  e.g. equations from Benjamin-Oro  Boussinesq  Hasegawa-Mima 
KdV-type  Klein-Gordon  NLS-type  Serre  Shamel   Whitham and Zakharov. This makes the book
interesting for professionals in the fields of nonlinear physics  applied mathematics and fluid
mechanics as well as students who are studying these subjects. The book can also be used as a
basis for a one-semester lecture course in applied mathematics or mathematical physics.

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