77 research outputs found
Field-asymmetric transverse magnetoresistance in a nonmagnetic quantum-size structure
A new phenomenon is observed experimentally in a heavily doped asymmetric
quantum-size structure in a magnetic field parallel to the quantum-well layers
- a transverse magnetoresistance which is asymmetric in the field (there can
even be a change in sign) and is observed in the case that the structure has a
built-in lateral electric field. A model of the effect is proposed. The
observed asymmetry of the magnetoresistance is attributed to an additional
current contribution that arises under nonequilibrium conditions and that is
linear in the gradient of the electrochemical potential and proportional to the
parameter characterizing the asymmetry of the spectrum with respect to the
quasimomentum.Comment: 10 pages, 5 figures. For correspondence, mail to
[email protected]
Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes
phenomenon for the second Painlev\'e equation . The
precise description of the exponentially small jump in the dominant solution
approaching as is given. For the asymptotic power
expansion of the dominant solution, the coefficient asymptotics is found.Comment: 19 pages, LaTe
On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation
Using a simple operator-norm estimate we show that the solution to the second
Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well
defined region of the complex plane of the independent variable. The result is
illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit
Quasi-linear Stokes phenomenon for the Painlev\'e first equation
Using the Riemann-Hilbert approach, the -function corresponding to the
solution of the first Painleve equation, , with the asymptotic
behavior as is constructed. The
exponentially small jump in the dominant solution and the coefficient
asymptotics in the power-like expansion to the latter are found.Comment: version accepted for publicatio
Hard loss of stability in Painlev\'e-2 equation
A special asymptotic solution of the Painlev\'e-2 equation with small
parameter is studied. This solution has a critical point corresponding to
a bifurcation phenomenon. When the constructed solution varies slowly
and when the solution oscillates very fast. We investigate the
transitional layer in detail and obtain a smooth asymptotic solution, using a
sequence of scaling and matching procedures
On the Linearization of the First and Second Painleve' Equations
We found Fuchs--Garnier pairs in 3X3 matrices for the first and second
Painleve' equations which are linear in the spectral parameter. As an
application of our pairs for the second Painleve' equation we use the
generalized Laplace transform to derive an invertible integral transformation
relating two its Fuchs--Garnier pairs in 2X2 matrices with different
singularity structures, namely, the pair due to Jimbo and Miwa and the one
found by Harnad, Tracy, and Widom. Together with the certain other
transformations it allows us to relate all known 2X2 matrix Fuchs--Garnier
pairs for the second Painleve' equation with the original Garnier pair.Comment: 17 pages, 2 figure
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