Nonlinear Dispersive Equations: Inverse Scattering and PDE Methods

Nonlinear Dispersive Equations are partial differential equations that arise in physical settings where dispersion dominates dissipation, and this monograph offers a thorough introduction to the topic, uniting the modeling, PDE, and integrable systems approaches. It focuses on three universal families of equations with a completely integrable member and presents numerical simulations to illustrate interesting phenomena.

Format: Paperback / softback
Length: 580 pages
Publication date: 25 February 2023
Publisher: Springer Nature Switzerland AG

Nonlinear dispersive equations (NDEs) are a class of partial differential equations (PDEs) that manifest in physical contexts where dispersion plays a dominant role over dissipation, particularly in the realms of hydrodynamics, nonlinear optics, plasma physics, and Bose-Einstein condensates. Traditionally, this topic has been approached from various angles, ranging from modeling physical phenomena to developing theories of partial differential equations and even as part of the theory of integrable systems. This monograph provides a comprehensive and in-depth exploration of NDEs, uniting the modeling, PDE, and integrable systems approaches for the first time in a single book. The presentation centers on three fundamental families of physically relevant equations that possess a fully integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are derived rigorously, and qualitative properties such as soliton resolution are examined in both integrable and non-integrable models. Throughout the text, numerical simulations are employed to illustrate captivating phenomena. By presenting and comparing results from diverse fields, the book aims to foster scientific interactions and attract new students and researchers to this captivating topic. To facilitate this, the chapters can be read largely independently of each other, and the prerequisites have been kept to introductory courses in PDE theory.

Weight: 908g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030914295
Edition number: 1st ed. 2021