Solitons 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. 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.