Search results for "KdV hierarchy"

showing 2 items of 2 documents

Wronskian Addition Formula and Darboux-Pöschl-Teller Potentials

2013

For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant.

Article SubjectWronskianlcsh:MathematicsGeneral MathematicsMathematics::Spectral TheoryEigenfunctionKdV hierarchylcsh:QA1-939Variation of parametersAction (physics)AlgebraKey pointNonlinear Sciences::Exactly Solvable and Integrable SystemsRepresentation (mathematics)MathematicsMathematical physicsJournal of Mathematics
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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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