Geometry and multidimensional soliton equations
type: Item
instance of: scholarly article
title: Geometry and multidimensional soliton equations
zbMATH Open document ID: 0981.37022
DOI: 10.1007/BF02557332
author: A. K. Danlybaeva
author: Ratbay Myrzakulov
author: Gulgasyl Nugmanova
published in: Theoretical and Mathematical Physics
publication date: 2002-05-27T00:00:00Z
review text: The connection between the differential geometry of curves and (2+1)-dimensional integrable systems is established. The Zakharov equation, the modified Veselov-Novikov equation, the modified Korteweg-de Vries equation, etc., are equivalent in the Lakshmanan sense to (2+1)-dimensional spin systems.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 1465891
MaRDI profile type: Publication
cites work: An elementary geometric characterization of the integrable motions of a curve
cites work: Method for Solving the Korteweg-deVries Equation
cites work: Q3732103
cites work: Q3995225
cites work: A soliton on a vortex filament
cites work: Solitons on moving space curves
cites work: Integrability and the motion of curves
cites work: Q3706107
cites work: Q4304304
cites work: A \((2+1)\)-dimensional integrable spin model: geometrical and gauge equivalent counterpart, solitons and localized coherent structures.
cites work: On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schrödinger equations
cites work: Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions
cites work: Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation
cites work: Benney equations and quasiclassical approximation in the method of the inverse problem
cites work: Some integrable hierarchies in (2+1) dimensions and their twistor description
cites work: Gauge equivalence between -dimensional continuous Heisenberg ferromagnetic models and nonlinear Schrödinger-type equations
Recommended article: Q3676791
Recommended article: Q4028079
Recommended article: On the geometry of soliton equations
Recommended article: Q4309540
Recommended article: Q3607415
Recommended article: Q4897017
Recommended article: Soliton equations and differential geometry
Recommended article: Geometry of solitons
Recommended article: Algebraic geometry of soliton equations
Recommended article: Q5371269
description: scientific article; zbMATH DE number 1465891