Quasiclassical generalized Weierstrass representation and dispersionless DS equation

TL;DR

This paper introduces a quasiclassical generalized Weierstrass representation for complex surfaces in four-dimensional space, linking it to the dispersionless Davey-Stewartson hierarchy, and explores its applications and extensions.

Contribution

It presents a novel quasiclassical GWR framework for highly corrugated surfaces and connects it to integrable dispersionless DS deformations, expanding the mathematical tools for surface analysis.

Findings

Proposed a new quasiclassical GWR for 4D surfaces.

Linked surface deformations to dispersionless DS hierarchy.

Discussed extensions to other 4D spaces and systems.

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.