This book gathers contributions on various aspects of the theory and
applications of linear and nonlinear waves and associated phenomena, as
well as approaches developed in a global partnership of researchers with
the national Centre of Excellence in Nonlinear Studies (CENS) at the
Department of Cybernetics of Tallinn University of Technology in
Estonia.
The papers chiefly focus on the role of mathematics in the analysis of
wave phenomena. They highlight the complexity of related topics
concerning wave generation, propagation, transformation and impact in
solids, gases, fluids and human tissues, while also sharing insights
into selected mathematical methods for the analytical and numerical
treatment of complex phenomena. In addition, the contributions derive
advanced mathematical models, share innovative ideas on computing, and
present novel applications for a number of research fields where both
linear and nonlinear wave problems play an important role.
The papers are written in a tutorial style, intended for non-specialist
researchers and students. The authors first describe the basics of a
problem that is currently of interest in the scientific community,
discuss the state of the art in related research, and then share their
own experiences in tackling the problem.
Each chapter highlights the importance of applied mathematics for
central issues in the study of waves and associated complex phenomena in
different media. The topics range from basic principles of wave
mechanics up to the mathematics of Planet Earth in the broadest sense,
including contemporary challenges in the mathematics of society. In
turn, the areas of application range from classic ocean wave mathematics
to material science, and to human nerves and tissues.
All contributions describe the approaches in a straightforward manner,
making them ideal material for educational purposes, e.g. for courses,
master class lectures, or seminar presentations.
