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Record Nr. |
UNINA9910624315703321 |
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Titolo |
Solitons / / edited by Mohamed Atef Helal |
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Pubbl/distr/stampa |
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New York, NY : , : Springer US : , : Imprint : Springer, , 2022 |
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ISBN |
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9781071624579 |
9781071624562 |
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Edizione |
[1st ed. 2022.] |
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Descrizione fisica |
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1 online resource (483 pages) |
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Collana |
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Encyclopedia of Complexity and Systems Science Series, , 2629-2343 |
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Disciplina |
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Soggetti |
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Plasma waves |
Mathematical physics |
Differential equations |
Environmental sciences |
Physics |
Fluid mechanics |
Waves, instabilities and nonlinear plasma dynamics |
Mathematical Methods in Physics |
Differential Equations |
Environmental Physics |
Engineering Fluid Dynamics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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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