Lagrangian 3-form structure for the Darboux system and the KP hierarchy
Frank Nijhoff
Abstract
Abstract A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the entire Kadomtsev–Petviashvili (KP) hierarchy in terms so-called Miwa variables. Thus, in providing a Lagrangian description of this multidimensionally consistent system amounts to a new Lagrangian 3-form structure for the continuous KP system. A generalisation to the matrix (also known as non-Abelian) KP system is discussed.
Topics & Concepts
HierarchyLagrangianCurvilinear coordinatesMathematicsCoordinate systemAlgebra over a fieldComplex systemPure mathematicsMatrix (chemical analysis)Abelian groupComputer scienceGeometryArtificial intelligenceMaterials scienceMarket economyEconomicsComposite materialNonlinear Waves and SolitonsNumerical methods for differential equationsNonlinear Photonic Systems