Geometrical optics in nonlinear media and integrable equations

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 dielectric constant on the frequency and fields gives rise to the dispersionless Veselov-Novikov equation for refractive index. It is demonstrated that the last one is amenable to the quasiclassical DBAR-dressing method. A connection is noted between geometrical optics phenomena under consideration and quasiconformal mappings on the plane.

10 pages, misprints corrected

References in corpus (10)

• 2D Gravity and Random Matrices
• Integrable Hierarchies and Dispersionless Limit
• Integrability and Matrix Models
• Integrable Structure of Interface Dynamics
• Conformal maps and dispersionless integrable hierarchies
• Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
• SDiff(2) KP hierarchy
• Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
• Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
• dbar-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy

Cited by in corpus (7)

• Integrable equations in nonlinear geometrical optics
• S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies
• On the r-th dispersionless Toda hierarchy I: Factorization problem, symmetries and some solutions
• 2-Soliton-solution of the Novikov-Veselov equation
• Symmetry constraints for real dispersionless Veselov-Novikov equation
• Lie reductions and exact solutions of dispersionless Nizhnik equation
• Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation