Solitons

ISBN-13: 9781071624562 / Angielski / Twarda / 2022 / 475 str.

Mohamed Atef Helal

Opis

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.

Spis treści

Nonlinear Water Waves and Nonlinear Evolution Equations with Applications

Inverse Scattering Transform and the Theory of Solitons

Korteweg-de Vries Equation (KdV), Different Analytical Methods for Solving the

Korteweg-de Vries Equation (KdV), History, Exact N-Soliton Solutions and Further Properties of the

Semi-analytical Methods for Solving the KdV and mKdV Equations

Korteweg-de Vries Equation (KdV), Some Numerical Methods for Solving the

Nonlinear Internal Waves

Partial Differential Equations that Lead to Solitons

Shallow Water Waves and Solitary Waves

Soliton Perturbation

Solitons and Compactons

Solitons: Historical and Physical Introduction

Solitons Interactions

Solitons, Introduction to

Solitons, Tsunamis and Oceanographical Applications of

Water Waves and the Korteweg-de Vries Equation

Soliton Solutions for Some Nonlinear Water Wave Dynamical Models

Analytical Soliton Solutions for Some Nonlinear Dynamical Water Waves Models

Soliton Propagation in Solids: Advances and Applications

Applications of lump and interaction soliton solutions to the model of liquid crystals and nerve fibers

Periodic cross-kink, rogue-waves, and lump interaction soliton solutions with kink and periodic waves for fractional Bogoyavlenskii equation

Double Tchebyshev spectral tau algorithm for solving KdV equation, with soliton application

O autorze

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.