Overview
- Elucidates the origin and properties of monster waves such as tsunamis
- Covers solitonic bio-energy transport
- Discusses governing equations that lead to tsunami, and their methods and solutions
Part of the book series: Encyclopedia of Complexity and Systems Science Series (ECSSS)
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About this book
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB.
The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
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Table of contents (22 entries)
Editors and Affiliations
About the editor
Mohamed Atef Helal received his BSc in Mathematics (with distinction 1st class honor in 1969) from the Faculty of Science, Cairo University, Egypt. He then received his MSc in Applied Mathematics from the Faculty of Science, Cairo University, in 1975. In 1976, he got his DEA from Institute de Mechanique (IMG) Grenoble, France. After that, he received his Doctorat 3ème Cycle in Fluid Mechanics from IMG, Grenoble, France, in 1979. Finally, he got his Ph.D. in Applied Mathematics from Cairo University in 1982. Mohamed is currently a Professor of Mathematics in the Faculty of Science, Cairo University. He is an active fellow in the Institute of Physics (England), Institute of Mathematics and its Applications (England), Royal Astronomical Society (England), and London Mathematical Society (England). Mohamed is also a member of several scientific societies in the USA and Europe. Mohamed also acted as a president of the Egyptian Mathematical and Physical Society and was a board member of the Egyptian Mathematical Society. Mohamed has various publications in different fields such as: non-linear partial differential equations and Soliton solutions, Tsunamis, computational fluid mechanics, physical oceanography, fluids in rotating circular basins, shallow water waves in stratified fluids, wavelets, induction in thin sheets, and its applications in oceans, dark energy and golden mean in cosmology and physics. Mohamed participated in writing and editing three books. He has guided many students who took up MSc and PhD in applied mathematics. He also participated in judging MSc and PhD theses from Egypt and other countries. He is an active reviewer in several well-known journals.
Bibliographic Information
Book Title: Solitons
Editors: Mohamed Atef Helal
Series Title: Encyclopedia of Complexity and Systems Science Series
DOI: https://doi.org/10.1007/978-1-0716-2457-9
Publisher: Springer New York, NY
eBook Packages: Physics and Astronomy, Reference Module Physical and Materials Science, Reference Module Chemistry, Materials and Physics
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2022
Hardcover ISBN: 978-1-0716-2456-2Published: 13 November 2022
eBook ISBN: 978-1-0716-2457-9Published: 12 November 2022
Series ISSN: 2629-2327
Series E-ISSN: 2629-2343
Edition Number: 1
Number of Pages: XXIV, 475
Number of Illustrations: 39 b/w illustrations, 112 illustrations in colour
Topics: Plasma Physics, Mathematical Methods in Physics, Analysis, Environmental Physics, Engineering Fluid Dynamics