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Nonlinear PDE Phenomena

In: Nonlinear Physics with Mathematica for Scientists and Engineers

Author

Listed:
  • Richard H. Enns

    (Simon Fraser University, Department of Physics)

  • George C. McGuire

    (University College of the Fraser Valley, Department of Physics)

Abstract

In Section 3.2.1 the reader encountered the Korteweg–deVries (KdV) equation which has been successfully used to describe the propagation of solitons in various physical contexts, the most historically famous being for shallow water waves in a rectangular canal. Using subscripts to denote partial derivatives with respect to the distance x traveled and the time t elapsed, the KdV equation for the (normalized) transverse displacement ψ of the water waves is 10.1 $${\psi _t} + \alpha \psi {\psi _x} + {\psi _{xxx}} = 0$$ .

Suggested Citation

  • Richard H. Enns & George C. McGuire, 2004. "Nonlinear PDE Phenomena," Springer Books, in: Nonlinear Physics with Mathematica for Scientists and Engineers, chapter 0, pages 413-450, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0211-0_10
    DOI: 10.1007/978-1-4612-0211-0_10
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