Letter to the Editor

doi:10.1088/0305-4470/37/10/L01

LETTER TO THE EDITOR

Geometrical optics in nonlinear media and integrable equations

Boris G Konopelchenko et al 2004 J. Phys. A: Math. Gen. 37 L105-L111 doi: 10.1088/0305-4470/37/10/L01

PDF (98.4 KB) | HTML | References | Articles citing this article

Boris G Konopelchenko and Antonio Moro
Dipartimento di Fisica dell'Università di Lecce and INFN, Sezione di Lecce, Via Arnesano, I-73100 Lecce, Italy
E-mail: konopel@le.infn.it and antonio.moro@le.infn.it

Abstract. It is shown that the geometrical optics limit of the Maxwell equations for certain nonlinear media with slow variation along one axis and particular dependence of the dielectric constant on frequency and fields gives rise to the dispersionless Veselov–Novikov equation for the refractive index. It is demonstrated that the dispersionless Veselov–Novikov hierarchy is amenable to the quasiclassical $\bar{\partial}$ -dressing method. A connection is noted between the geometrical optics phenomena under consideration and the quasiconformal mappings on the plane.

PACS numbers: 02.30.Ik, 42.15.Dp

Print publication: Issue 10 (12 March 2004)
Received 5 January 2004
Published 24 February 2004

Post to CiteUlike |

Post to Connotea |

Post to Bibsonomy

Geometrical optics in nonlinear media and integrable equations

Find related articles

Article options

Authors & Referees