LEADER 04337nam 22007095 450 001 9910624315703321 005 20230822192912.0 010 $a9781071624579$b(electronic bk.) 010 $z9781071624562 024 7 $a10.1007/978-1-0716-2457-9 035 $a(MiAaPQ)EBC7135420 035 $a(Au-PeEL)EBL7135420 035 $a(CKB)25315244800041 035 $a(DE-He213)978-1-0716-2457-9 035 $a(PPN)266352553 035 $a(EXLCZ)9925315244800041 100 $a20221112d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSolitons /$fedited by Mohamed Atef Helal 205 $a1st ed. 2022. 210 1$aNew York, NY :$cSpringer US :$cImprint: Springer,$d2022. 215 $a1 online resource (483 pages) 225 1 $aEncyclopedia of Complexity and Systems Science Series,$x2629-2343 311 08$aPrint version: Helal, Mohamed Atef Solitons New York, NY : Springer,c2022 9781071624562 320 $aIncludes bibliographical references and index. 327 $aNonlinear 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. 330 $aThis newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger?s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies. 410 0$aEncyclopedia of Complexity and Systems Science Series,$x2629-2343 606 $aPlasma waves 606 $aMathematical physics 606 $aDifferential equations 606 $aEnvironmental sciences 606 $aPhysics 606 $aFluid mechanics 606 $aWaves, instabilities and nonlinear plasma dynamics 606 $aMathematical Methods in Physics 606 $aDifferential Equations 606 $aEnvironmental Physics 606 $aEngineering Fluid Dynamics 615 0$aPlasma waves. 615 0$aMathematical physics. 615 0$aDifferential equations. 615 0$aEnvironmental sciences. 615 0$aPhysics. 615 0$aFluid mechanics. 615 14$aWaves, instabilities and nonlinear plasma dynamics. 615 24$aMathematical Methods in Physics. 615 24$aDifferential Equations. 615 24$aEnvironmental Physics. 615 24$aEngineering Fluid Dynamics. 676 $a530.124 702 $aHelal$b Mohamed Atef 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910624315703321 996 $aSolitons$92968384 997 $aUNINA