1,958 research outputs found
Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlev\'e equations P and P
We study reductions of the Korteweg--de Vries equation corresponding to
stationary equations for symmetries from the noncommutative subalgebra. An
equivalent system of second-order equations is obtained, which reduces to
the Painlev\'e equation P for . On the singular line , a
subclass of special solutions is described by a system of second-order
equations, equivalent to the P equation for . For these systems, we
obtain the isomonodromic Lax pairs and B\"acklund transformations which form
the group .Comment: 11 page
Planar Heterostructure Graphene -- Narrow-Gap Semiconductor -- Graphene
We investigate a planar heterostructure composed of two graphene films
separated by a narrow-gap semiconductor ribbon. We show that there is no the
Klein paradox when the Dirac points of the Brillouin zone of graphene are in a
band gap of a narrow-gap semiconductor. There is the energy range depending on
an angle of incidence, in which the above-barrier damped solution exists.
Therefore, this heterostructure is a "filter" transmitting particles in a
certain range of angles of incidence upon a potential barrier. We discuss the
possibility of an application of this heterostructure as a "switch".Comment: 9 pages, 2 figure
Interface states in junctions of two semiconductors with intersecting dispersion curves
A novel type of shallow interface state in junctions of two semiconductors
without band inversion is identified within the envelope function
approximation, using the two-band model. It occurs in abrupt junctions when the
interband velocity matrix elements of the two semiconductors differ and the
bulk dispersion curves intersect. The in-plane dispersion of the interface
state is found to be confined to a finite range of momenta centered around the
point of intersection. These states turn out to exist also in graded junctions,
with essentially the same properties as in the abrupt case.Comment: 1 figur
Graded associative conformal algebras of finite type
In this paper, we consider graded associative conformal algebras. The class
of these objects includes pseudo-algebras over non-cocommutative Hopf algebras
of regular functions on some linear algebraic groups. In particular, an
associative conformal algebra which is graded by a finite group is a
pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group
such that the identity component is the affine line and . A classification of simple and semisimple graded associative
conformal algebras of finite type is obtained
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