Hydrodynamic and Optical Waves: A Common Approach for Unidimensional Propagation
Authors: Onorato M., Baronio F., Conforti M., Chabchoub A., Suret P., Randoux S.
Autors Affiliation: Univ Torino, Dipartimento Fis, IT-10125 Turin, Italy; INFN, Sez Torino, IT-10125 Turin, Italy; Univ Brescia, INO, CNR, Via Branze 38, I-25123 Brescia, Italy; Univ Brescia, Dipartimento Ingn Informaz, Via Branze 38, I-25123 Brescia, Italy; Univ Lille, CNRS, UMR PhLAM Phys Lasers Atomes & Mol 8523, F-59000 Lille, France; Univ Tokyo, Dept Ocean Technol Policy & Environm, Grad Sch Frontier Sci, Kashiwa, Chiba 2778563, Japan; Aalto Univ, Dept Mech Engn, Sch Engn, FI-02150 Espoo, Finland; Univ Lille 1, Lab Phys Lasers Atomes & Mol, UMR CNRS 8523, Sci & Technol,France Ctr Etud & Rech Laser & Appl, F-59655 Villeneuve Dascq, France
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: HAMILTONIAN THEORY; ZAKHAROV EQUATION; GRAVITY-WAVES; CONSEQUENCES; SURFACE