Nonlinear Dispersive Equations : Inverse Scattering and PDE Methods Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation notably hydrodynamics nonlinear optics plasma physics and Bose–Einstein condensates. The topic has traditionally been approached in different ways from the perspective of modeling of physical phenomena to that of the theory of partial differential equations or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic uniting the modeling PDE and integrable systems approaches for the first time in book form. The presentation focuses on three universal families of physically relevant equations endowed with a completely integrable member: the Benjamin–Ono Davey–Stewartson and Kadomtsev–Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory. Acronyms Glossary 1 General Introduction 2 Generalities and Basic Facts 3 Benjamin–Ono and Intermediate Long Wave Equations: Modeling IST and PDE 4 Davey–Stewartson and Related Systems 5 Kadomtsev–Petviashvili and Related Equations 6 Novikov–Veselov and Derivative Nonlinear Schrödinger Equations Index.