Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations

We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants. Further, the parabolic, soliton and breather solutions of the GI equation are given as explicit examples.Comment: 16 pages, 4 figure

Invariants of hyperbolic partial differential operators

We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order

On Darboux transformations for the derivative nonlinear Schr\"odinger equation

We consider Darboux transformations for the derivative nonlinear Schr\"odinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented and proved. The solution is expressed in quasideterminant forms. Additionally, the parabolic and soliton solutions of the derivative nonlinear Schr\"odinger equation are given as explicit examples.Comment: 14 page

Twisted laplace maps

We consider general Darboux maps arising from intertwining relations on second order, linear partial differential operators, as deformations of the classical, Laplace case. We present Lax pairs for the corresponding relations on invariants and discuss the conditions for a lattice structure analogous to 2D Toda theory

Effects of adrenalin on ovarian injury formed by ischemia reperfusion in rats

In this study, the impacts of adrenalin on ovarian injury caused by ischemia reperfusion were investigated in rats. In addition, it’s been investigated whether there is a correlation between adrenergic receptors and oxidant/anti-oxidant and COX1/COX-2 levels. It’s been observed that the COX-2 level that is responsible for MDA and inflammatory reaction (which are the indicators of oxidative stress in ovarian tissue to which ischemia reperfusion was applied) increased and the COX-1 levels that are responsible for GSH (an endogenic anti-oxidant with protective impact) were depressed. Adrenalin has prevented an increase in MDA and COX-2 activity in the ovarian tissue, to which I/R was applied, and prevented a reduction in GSH and COX-1 activity. However, adrenalin failed to prevent an MDA increase in ovarian tissue, to which alpha-2 adrenergic receptor blocker yohimbine was given (I/R formed), and also failed to prevent a GSH and COX-1 decrease. Adrenalin also failed to inhibit the COX-2 activity increase in ovarian tissue, to which beta blocker was applied. As a result, stimulation of the alpha-2 adrenergic receptors in an ovarian tissue causes an anti-oxidant and protective effect, while stimulation of beta-2 adrenergic receptors causes an anti-inflammatory effect. It’s been thought that adrenalin protects the ovarian tissue against ischemia reperfusion by stimulating the alpha-2 and beta-2 adrenergic receptors.Colegio de Farmacéuticos de la Provincia de Buenos Aire

Evolution equations for differential invariants

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Quasi-Grammian solutions of the coupled Gerdjikov-Ivanov equation

We construct the N-fold standard binary Darboux transformation (bDT) for the coupled Gerdjikov–Ivanov (cGI) equation. Then, using the bDT presented in this article, we explicitly construct the exact solutions of the cGI equation in terms of quasi-Grammians. As applications of the bDT, we present various particular solutions for the cGI equation, including soliton, breather, and rogue wave solutions

Binary Darboux transformation for the Gerdjikov–Ivanov equation

We present a standard binary Darboux transformation for the Gerdjikov–Ivanov equation and then construct its quasigrammian solutions. Further, the multi-soliton, breather and rogue wave solutions of the Gerdjikov–Ivanov equation are given as particular examples