Applied Wave Mathematics II

Selected Topics in Solids, Fluids, and Mathematical Methods and Complexity

  • Arkadi Berezovski
  • Tarmo Soomere

Part of the Mathematics of Planet Earth book series (MPE, volume 6)

Table of contents

  1. Front Matter
    Pages i-xxxiii
  2. Linear Waves

  3. Nonlinear Waves

    1. Front Matter
      Pages 39-39
    2. Tomas Torsvik, Ahmed Abdalazeez, Denys Dutykh, Petr Denissenko, Ira Didenkulova
      Pages 41-60
    3. Oxana Kurkina, Andrey Kurkin, Efim Pelinovsky, Yury Stepanyants, Tatiana Talipova
      Pages 61-87
    4. Andrus Salupere, Martin Lints, Lauri Ilison
      Pages 89-124
    5. Karima R. Khusnutdinova, Matthew R. Tranter
      Pages 125-150
    6. Alexey V. Porubov, Alena E. Osokina
      Pages 151-166
    7. Tommaso Ruggeri, Shigeru Taniguchi
      Pages 167-186
  4. Modelling and Mathematics

    1. Front Matter
      Pages 205-205
    2. Tanel Peets, Kert Tamm
      Pages 207-238
    3. Harm Askes, Dario De Domenico, Mingxiu Xu, Inna M. Gitman, Terry Bennett, Elias C. Aifantis
      Pages 239-255
    4. Mihhail Berezovski, Arkadi Berezovski
      Pages 257-280
    5. Mihhail Berezovski, Stan Elektrov, Konstantin Lurie
      Pages 281-303
    6. Domènec Ruiz-Balet, Enrique Zuazua
      Pages 343-363
  5. Back Matter
    Pages 371-376

About this book


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.


fluid dynamics waves in solids linear waves nonlinear waves shock waves internal waves surface waves elastic waves, solitons finite-difference scheme material science graphene phase field theory microstructured medium

Editors and affiliations

  • Arkadi Berezovski
    • 1
  • Tarmo Soomere
    • 2
  1. 1.Department of Cybernetics, School of ScienceTallinn University of TechnologyTallinnEstonia
  2. 2.Department of Cybernetics, School of ScienceTallinn University of Technology, Tallinn, Estonia, Estonian Academy of SciencesTallinnEstonia

Bibliographic information