Differential Galois theory and Darboux transformations for Integrable Systems
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DOI: 10.1016/j.geomphys.2016.06.016
Abstract: Abstract We apply the Differential Galois Theory of linear partial differential systems to the Backlund–Darboux transformations of the AKNS solitonic partial differential equations. We prove that the Galois group of the transformed system is isomorphic… read more here.
Keywords: galois theory; theory darboux; differential galois; darboux transformations ... See more keywords
Higher dimensional Darboux transformations
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DOI: 10.1016/j.jmaa.2018.04.031
Abstract: Abstract We give conditions for a first order partial differential operator to serve as an n-dimensional Darboux transformation between two second-order partial differential operators. We show that some of these conditions are given by first… read more here.
Keywords: order; partial differential; darboux; darboux transformations ... See more keywords
Super integrable hierarchies associated with spl(2, 1) and Darboux transformations
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DOI: 10.1063/1.5018031
Abstract: Based on the Lie superalgebra spl(2, 1) and the TAH scheme, we generate (1+1)-dimensional and (2+1)-dimensional super soliton hierarchies associated with spl(2, 1). And by using the super-trace identity on Lie superalgebras, we construct the… read more here.
Keywords: associated spl; super soliton; integrable hierarchies; super integrable ... See more keywords
Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class
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DOI: 10.1063/5.0013832
Abstract: We construct Darboux transformations of arbitrary order for generalized Schrodinger-type equations, the potentials of which are second-degree polynomials in the energy. Our equations are allowed to contain first-derivative terms with arbitrary coefficients, such as they… read more here.
Keywords: darboux transformations; generalized schr; heun class; energy ... See more keywords