Search results for "Grassmannian"

showing 2 items of 12 documents

The Kp Hierarchy

1989

As an application of the theory of infinite-dimensional Grassmannians and the representation theory of gl1 we shall study in this chapter certain nonlinear “exactly solvable” systems of differential equations. Exactly solvable means here that the nonlinear system can be transformed to an (infinite-dimensional) linear problem. A prototype of the equations is the Korteweg-de Vries equation $$\frac{{\partial u}}{{\partial t}} = \frac{3}{3}u\frac{{\partial u}}{{\partial x}} + \frac{1}{4}\frac{{{\partial ^3}u}}{{\partial {x^3}}}$$ . It turns out that it is more natural to consider an infinite system of equations like that above, for obtaining explicit solutions. The set of equations is called th…

Set (abstract data type)Pure mathematicsNonlinear systemNonlinear Sciences::Exactly Solvable and Integrable SystemsHierarchy (mathematics)Differential equationGrassmannianKdV hierarchySystem of linear equationsRepresentation theoryMathematics
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On double Veronese embeddings in the Grassmannian G(1,N)

2004

We classify all the embeddings of P^n in a Grassmannian of lines G(1,N) such that the composition with Pl\"ucker is given by a linear system of quadrics of P^n.

Veronese embeddingsGeneral MathematicsLinear systemComposition (combinatorics)CombinatoricsAlgebra14M15 (Primary) 14M07 (Secondary)rank-2 bundlesMathematics - Algebraic GeometryGrassmannianFOS: MathematicsSettore MAT/03 - GeometriaGrassmanniansPluckerAlgebraic Geometry (math.AG)Mathematics
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