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.


Solitary Wave Internal Wave Inverse Scattering Solitary Wave Solution Internal Solitary Wave 
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© CISM, Udine 2005

Authors and Affiliations

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

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