Reduction of the Self-dual Yang-Mills Equations to Sinh-Poisson Equation and Exact Solutions
Gharib. M. Gharib, Rania Saadeh
Abstract
The geometric properties of differential systems are used to demonstrate how the sinh-poisson equation describes a surface with a constant negative curvature in this paper. The canonical reduction of 4-dimensional self dual Yang Mills theorem is the sinh-poisson equation, which explains pseudo spherical surfaces. We derive the B¨acklund transformations and the travelling wave solution for the sinh-poisson equation in specific. As a result, we discover exact solutions to the self-dual Yang-Mills equations.
Topics & Concepts
Hyperbolic functionMathematicsUniqueness theorem for Poisson's equationMathematical analysisPoisson distributionPoisson's equationPartial differential equationDual (grammatical number)CurvatureDifferential equationMathematical physicsGeometryUniquenessStatisticsLiteratureArtNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Fiber Laser Technologies