Hydrodynamic and Optical Waves: A Common Approach for Unidimensional Propagation

  • Miguel Onorato
  • Fabio Baronio
  • Matteo Conforti
  • Amin Chabchoub
  • Pierre Suret
  • Stephane Randoux
Chapter
First Online:
Part of the Lecture Notes in Physics book series (LNP, volume 926)

Abstract

The aim of this chapter is to build a bridge between water and optical waves. After a brief introduction on the role played by the so-called normal variable in the D’Alembert equation and a short description of the Hamiltonian formulation of water waves, we introduce a similar formalism for describing optical waves. We restrict our analysis to one-dimensional propagation. Under a number of assumptions, we rewrite the Maxwell equations in a very general form that account for three- and four-wave interactions. Those equations are very similar to the one describing water waves. Analogies and differences between hydrodynamic and optical waves are also discussed.

Keywords

Dispersion Relation Water Wave Canonical Transformation Rogue Wave Optical Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

Miguel Onorato and Fabio Baronio were supported by MIUR Grant PRIN 2012BFNWZ2. Dr. B. Giulinico and F. Giardini are also acknowledged for discussions during the early stages of this work. Amin Chabchoub acknowledges support from the Burgundy Region, The Association of German Engineers (VDI) and the Japan Society for the Promotion of Science (JSPS).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Miguel Onorato
    • 1
    • 2
  • Fabio Baronio
    • 3
  • Matteo Conforti
    • 4
  • Amin Chabchoub
    • 5
    • 6
  • Pierre Suret
    • 7
  • Stephane Randoux
    • 7
  1. 1.Dipartimento di FisicaUniversità degli Studi di TorinoTorinoItaly
  2. 2.Istituto Nazionale di Fisica NucleareINFN, Sezione di TorinoTorinoItaly
  3. 3.INO CNR and Dipartimento di Ingegneria dell’InformazioneUniversità di BresciaBresciaItaly
  4. 4.Univ. Lille, CNRSUMR 8523 - PhLAM - Physique des Lasers Atomes et MoléculesLilleFrance
  5. 5.Department of Ocean Technology Policy and EnvironmentGraduate School of Frontier Sciences, The University of TokyoKashiwa, ChibaJapan
  6. 6.Department of Mechanical Engineering, School of EngineeringAalto UniversityEspooFinland
  7. 7.Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Université de Lille I, Sciences et TechnologiesFrance Centre d’Etudes et de Recherches Lasers et Applications (CERLA)Villeneuve d’AscqFrance

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