Atmospheric free fall with quadratic resistance when considered from the point of view of the strictly isospectral construction of supersymmetric quantum mechanics is a powerful analogy for the class of Darboux cosmological fluids that I introduced in a previous work. Here, using this analogy, it is shown that the possible accelerating cosmological effects are due to the quadratic negative fric...

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillator with a homogeneous cubic-polynomial potential and the perturbed harmonic oscillator with a hom...

We present a new approach to the construction of the Darboux matrix. This is a generalization of the recently formulated method based on the assumption that the square of the Darboux matrix vanishes for some values of the spectral parameter. We consider the multisoliton case, the reduction problem and the discrete case. The relationship between our approach and the standard dressing method is d...

In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. We define the class of potentials that are invariant under the Darboux – Crum transformations and prove a number of lemmas and theorems substantiating the formulated formerly conjectures o...

Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N = 2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one type of surface operators the corresponding 2d theory is the WZW model, and for another type — the Liouville theory with insertions of extra degenerate fields...

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generali...

A Darboux transformation is constructed for the modified Veselov-Novikov equation .

STABILITY AND SENSITIVITY OF DARBOUX TRANSFORMATION WITHOUT PARAMETER M. ISABEL BUENO AND FROILÁN M. DOPICO Abstract. The monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. Darboux transformation without parameter changes a monic Jacobi matrix associa...

In this article, we examine the relationship between Darboux frames along parameter curves and frame of base curve ruled surface. We derive equations quaternionic shape operators, which can rotate tangent vectors around normal vector, find corresponding rotation matrices. Using these Gauss curvature mean explore how properties are found by use Frenet instead generator vectors. provide illustrat...