Using the (generalized) Darboux transformation in the case of the Clifford torus, we construct for all Pythagorean triples (p, q, n) ∈ Z a CP–family of Willmore tori in S with Willmore energy 2nπ.

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and s...

We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The hierarchies in question generalize those constructed by Chen, Kontsevich and Schwarz [40] for the WDVV equations. As a byproduct, we obtain a Darboux-type transformation and a (conditional) Bäcklund transformation for the...

The Grammian determinant type solutions of the KP hierarchy, obtained through the vectorial binary Darboux transformation, are reduced, imposing suitable differential constraint on the transformation data, to Pfaffian solutions of the BKP hierarchy. On leave of absence from Beijing Graduate School, CUMT, Beijing 100083, China Supported by Beca para estancias temporales de doctores y tecnólogos ...

The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and method additional independent variables. Then symmetric reduction presented. In order to provide a simpler version resulting we introduce $\tau/\sigma$ form (commutative) system. Our give, in continuous limit, classical

A method is presented to obtain the change in potential and relevant wavefunction of a linear system ordinary differential equations containing spectral parameter, when that perturbed finite number discrete eigenvalues are added or removed from spectrum. Some explicit formulas derived for those changes by introducing certain fundamental integral corresponding unperturbed systems. This generaliz...