Korteweg de-Vries Equation

  • Roger Grimshaw
Chapter
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 483)

Abstract

In this chapter we consider weakly nonlinear long waves. Here the basic paradigm is the well-known Korteweg-de Vries equation and its solitary wave solution. We present a brief historical discussion, followed by a typical derivation in the context of internal and surface water waves. Then we describe two extensions, the first to the variable-coefficient Korteweg-de Vries equation for the description of solitary waves in a variable environment, and the second to the forced Korteweg-de Vries equation and the theory of undular bores.

Keywords

Solitary Wave Internal Wave Inverse Scattering Solitary Wave Solution Internal Solitary Wave 
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Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Roger Grimshaw
    • 1
  1. 1.Department of Mathematical SciencesLoughborough UniversityUK

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