Quasiclassical generalized Weierstrass representation and dispersionless DS equation

Abstract

Quasiclassical generalized Weierstrass representation (GWR) for highly corrugated surfaces with slow modulation in the four-dimensional Euclidean space is proposed. Integrable deformations of such surfaces are described by the dispersionless Davey-Stewartson hierarchy. Quasiclassical GWRs for other four-dimensional spaces and dispersionless DS system are discussed too.

13 pages, talk given at the workshop "Solitons, collapses and turbulence",May 15-17, 2007, Chernogolovka, Russia

References in corpus (4)

• Generalized Weierstrass-Enneper inducing, conformal immersions, and gravity
• Parallel and Perpendicular Lamellae on Corrugated Surfaces
• Quantum effects for extrinsic geometry of strings via the generalized Weierstrass representation
• Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

Cited by in corpus (4)

• Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
• On the dispersionless Davey-Stewartson system: Hamiltonian vector fields Lax pair and relevant nonlinear Riemann-Hilbert problem for dDS-II system
• Coisotropic deformations of algebraic varieties and integrable systems
• Hamiltonian motions of plane curves and formation of singularities and bubbles