93 research outputs found
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
here is
the unknown function depends on one discrete and one continuous
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
Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries
The work deals with the qualification of semidiscrete hyperbolic type
equations. We study a class of equations of the form
here the
unknown function depends on one discrete and one continuous
variables. Qualification is based on the requirement of the existence of higher
symmetries. The case is considered when the symmetry is of order 5 in
continuous directions. As a result, a list of four equations with the required
conditions is obtained. For one of the found equations, a Lax representation is
constructed.Comment: 11 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
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