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Asymptotic Equations for Nonlinear Hyperbolic Waves

In: Surveys in Applied Mathematics

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  • John K. Hunter

    (University of California, Department of Mathematics and Institute of Theoretical Dynamics)

Abstract

Universal asymptotic equations. It is a remarkable fact that, in suitable asymptotic limits, the behavior of almost all nonlinear waves is described by a few rather simple looking nonlinear equations. Examples include Burgers equation, the Kortewegde Vries (KdV) equation, and the nonlinear Schrodinger equation. These equations are “universal” or “canonical” because their applicability depends only on a few, very general features of the wave motion, such as the form of the linearized dispersion relation and the type of nonlinearity acting on the wave. Universal equations thus provide a common theoretical core for the study of nonlinear waves in an enormous number of diverse physical systems.

Suggested Citation

  • John K. Hunter, 1995. "Asymptotic Equations for Nonlinear Hyperbolic Waves," Springer Books, in: Surveys in Applied Mathematics, chapter 3, pages 167-276, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1991-1_3
    DOI: 10.1007/978-1-4615-1991-1_3
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