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Whitham Modulation Equations and Application to Small Dispersion Asymptotics and Long Time Asymptotics of Nonlinear Dispersive Equations

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Rogue and Shock Waves in Nonlinear Dispersive Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 926))

Abstract

In this chapter we review the theory of modulation equations or Whitham equations for the travelling wave solution of KdV. We then apply the Whitham modulation equations to describe the long-time asymptotics and small dispersion asymptotics of the KdV solution.

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Acknowledgements

Tamara Grava acknowledges the support by the Leverhulme Trust Research Fellowship RF-2015-442 from UK and PRIN Grant “Geometric and analytic theory of Hamiltonian systems in finite and infinite dimensions” of Italian Ministry of Universities and Researches.

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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Tamara Grava

  2. Mathematic Area, SISSA, Via Bonomea 265, 34100, Trieste, Italy

    Tamara Grava

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  1. Tamara Grava
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Correspondence to Tamara Grava .

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Editors and Affiliations

  1. Dipartimento di Fisica, Università di Torino, Torino, Italy

    Miguel Onorato

  2. Institut Non Linéaire de Nice, Centre National de la Recherche Scientifique, CNRS, Université de Nice-Sophia Antipolis, Valbonne, France

    Stefania Resitori

  3. Dipartimento di Ingegneria dell' Informazione, Università di Brescia, Brescia, Italy

    Fabio Baronio

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Grava, T. (2016). Whitham Modulation Equations and Application to Small Dispersion Asymptotics and Long Time Asymptotics of Nonlinear Dispersive Equations. In: Onorato, M., Resitori, S., Baronio, F. (eds) Rogue and Shock Waves in Nonlinear Dispersive Media. Lecture Notes in Physics, vol 926. Springer, Cham. https://doi.org/10.1007/978-3-319-39214-1_10

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