Construction and separability of nonlinear soliton integrable couplings

A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of Wen-Xiu Ma et al. (Comp. Math. Appl. 60 (2010) 2601, Appl. Math. Comp. 217 (2011) 7238), where new class of soliton systems, being nonlinear integrable couplings, was introduced. The general form of solutions of the considered class of coupled systems is described. Moreover, the decoupling procedure is derived, which is also applicable to several other coupling systems from the literature.Comment: letter, 10 page

Maximal superintegrability of Benenti systems

For a class of Hamiltonian systems naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional integrals of motion.Comment: 5 pages, LaTeX 2e, to appear in J. Phys. A: Math. Ge

On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page

Patients’ Radiation Doses During the Implantation of Stents in Carotid, Renal, Iliac, Femoral and Popliteal Arteries

AbstractObjectives and DesignThe aim of the study was to document the radiation doses to patients during the implantation of stents in various arteries and to discuss potential reasons for prolongation of radiological procedures.Materials and MethodsMeasurements of air kerma (Gy) and dose–area product (Gy cm2) (DAP) were carried out simultaneously on a sample of 345 patients, who underwent different interventional radiological procedures involving angioplasty with stenting of 73 carotid (21.5%), 22 renal (6.5%), 160 iliac (45%), 63 femoral (18.6%) and 27 popliteal (7.9%) arteries.ResultsThe highest mean air kerma values for fluoroscopy and exposure were found for renal angioplasty (340 and 420 mGy, respectively). With regard to total DAP values, the highest were obtained for renal (148 Gy cm2) and iliac/The Inter-Society Consensus for Management of Peripheral Arterial Disease (TASC) II C (199 Gy cm2) stent implantation. The lowest values were for carotid (53 Gy cm2), iliac/TASC II A (6.3 Gy cm2) and femoral/TASC II A (53 Gy cm2) arteries. For 3.5% of the patients, the air kerma was between 1 and 1.5 Gy and for 1.5%, it was between 1.5 and 2 Gy.ConclusionsIn procedures performed on the arteries of the lower limbs, a significantly higher dose was received by patients with TASC II C lesions. With regard to the number of stents implanted, the total DAP value was 50% higher for simultaneous three-stent implantation than for one or two stents

Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless Lax pairs and an infinity of hydrodynamic reductions.Comment: 34 page

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page

Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory

A systematic way of construction of (1+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the classical R-matrix on Poisson algebras of formal Laurent series. Results are illustrated with the known and new (1+1)-dimensional dispersionless systems.Comment: 23 page