Solitons / Mohamed Atef Helal, editor.

Format:

Book

Contributor:

Helal, Mohamed Atef, editor.

Series:

Encyclopedia of complexity and systems science series ; second edition.

Encyclopedia of complexity and systems science series

Language:

English

Subjects (All):

Solitons.

Genre:

Electronic books.

Physical Description:

1 online resource (xxiv, 475 pages) : illustrations (chiefly color).

Place of Publication:

New York : Springer, [2022]

Summary:

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 Schrodinger (NLS), Korteweg-de-Vries Burgers (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.

Contents:

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

Tsunamis and Oceanographical Applications of Solitons.

Notes:

"A volume in the Encyclopedia of complexity and systems science, second edition."

Includes index.

Print version record.

Other Format:

Print version: Solitons.

ISBN:

9781071624579

1071624571

OCLC:

1350793147

Access Restriction:

Restricted for use by site license.