Twistor correspondences for the soliton hierarchies

DOI10.1016/0393-0440(92)90051-2zbMath0745.32016OpenAlexW2090085846MaRDI QIDQ1184386

Lionel J. Mason, George A. J. Sparling

Publication date: 28 June 1992

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(92)90051-2

zbMATH Keywords

integrable systemssymmetry reductiontwistorssoliton hierarchiesYang-Mills equationsKorteweg de Vries (KdV) equationsnon-linear Schrödinger (NS) equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Yang-Mills and other gauge theories in quantum field theory (81T13) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Twistor theory, double fibrations (complex-analytic aspects) (32L25) Applications of holomorphic fiber spaces to the sciences (32L81)

Related Items

Nonabelian KP hierarchy with Moyal algebraic coefficients ⋮ The twistor theory of equations of KdV type. I ⋮ Non-commutative Ward's conjecture and integrable systems ⋮ Two-dimensional integrable systems and self-dual Yang–Mills equations ⋮ Optical soliton solutions to a \((2+1)\) dimensional Schrödinger equation using a couple of integration architectures ⋮ A twistor-inspired Darboux transform for the sine–Gordon equation ⋮ Scattering of noncommutative waves and solitons in a supersymmetric chiral model in \(2 + 1\) dimensions ⋮ Lax pairs of integrable equations in \(1\leq d\leq 3\) dimensions as reductions of the Lax pair for the self-dual Yang-Mills equations ⋮ Tau functions and the twistor theory of integrable systems. ⋮ A geometry for multidimensional integrable systems ⋮ Twistor theory at fifty: from contour integrals to twistor strings ⋮ Conformal field theories in six-dimensional twistor space ⋮ The structure of all extended supersymmetric self-dual gauge theories ⋮ Some integrable hierarchies in (2+1) dimensions and their twistor description ⋮ Twistor reductions of the KdV hierarchy ⋮ The Landau-Lifshitz equation, elliptic curves and the Ward transform ⋮ Manifolds with an $SU(2)$-action on the tangent bundle ⋮ Darboux Transformations, Higher-Order Rational Solitons and Rogue Wave Solutions for a (2 + 1)-Dimensional Nonlinear Schrödinger Equation ⋮ Infinite conformal algebras in supersymmetric theories on four-manifolds ⋮ Reductions by isometries of the self-dual Yang–Mills equations in four-dimensional Euclidean space ⋮ A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear integrable equations. Recursion operators, group-theoretical and Hamiltonian structures of soliton equations
• Monopoles and geodesics
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Nonlinear gravitons and curved twistor theory
• Stationary axisymmetric space-times: A new approach
• Integrable and solvable systems, and relations among them
• The Nahm equations, finite-gap potentials and Lame functions
• The Geroch group and non-Hausdorff twistor spaces
• Method for Solving the Korteweg-deVries Equation
• Twistor description of the symmetries of Einstein's equations for stationary axisymmetric spacetimes
• On self-dual gauge fields

This page was built for publication: Twistor correspondences for the soliton hierarchies