Classification of five-point differential-difference equations

Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes such well-known examples as the Itoh-Narita-Bogoyavlensky and the discrete Sawada-Kotera equations. The resulting list contains 17 equations some of which seem to be new. We have found non-point transformations relating most of the resulting equations among themselves and their generalized symmetries.Comment: 29 page

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.Comment: 27 page

Classification of semidiscrete hyperbolic type equations. The case of third order symmetries

In this paper, a classification of semidiscrete equations of hyperbolic type is carried out. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here is the unknown function $u_n (x)$ depends on one discrete $n$ and one continuous $x$ variables. The classification is based on the requirement for the existence of higher symmetries in the discrete and continuous directions. The case is considered when the symmetries are of order 3 in both directions. As a result, a list of equations with the required conditions is obtained.Comment: 14 pages (in Russian

Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation

We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.Comment: 13 pages, 3 figure

Experimental Observation of the Inverse Proximity Effect in Superconductor/Ferromagnet Layered Structures

We have studied the nuclear magnetic resonance (NMR) of 51V nuclei in the superconductor/ferromagnet thin film heterostructures Ni/V/Ni and Pd{1-x}Fe{x}/V/Pd{1-x}Fe{x} in the normaland superconducting state. Whereas the position and shape of the NMR line in the normal state for the trilayers is identical to that observed in a single V-layer, in the superconducting state the line shape definitely changes, developing a systematic distortion of the high-field wing of the resonance line. We consider this as the first experimental evidence for the penetration of ferromagnetism into the superconducting layer, a phenomenon which has been theoretically predicted recently and dubbed the inverse proximity effect.Comment: about 5 pages, 3 figures, 1 tabl

Full spin switch effect for the superconducting current in a superconductor/ferromagnet thin film heterostructure

Superconductor/ferromagnet (S/F) proximity effect theory predicts that the superconducting critical temperature of the F1/F2/S or F1/S/F2 trilayers for the parallel orientation of the F1 and F2 magnetizations is smaller than for the antiparallel one. This suggests a possibility of a controlled switching between the superconducting and normal states in the S layer. Here, using the spin switch design F1/F2/S theoretically proposed by Oh et al. [Appl. Phys. Lett. 71, 2376 (1997)], that comprises a ferromagnetic bilayer separated by a non-magnetic metallic spacer layer as a ferromagnetic component, and an ordinary superconductor as the second interface component, we have successfully realized a full spin switch effect for the superconducting current.Comment: 5 pages, 4 figure