785 research outputs found
Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations
Meromorphic solutions of autonomous nonlinear ordinary differential equations
are studied. An algorithm for constructing meromorphic solutions in explicit
form is presented. General expressions for meromorphic solutions (including
rational, periodic, elliptic) are found for a wide class of autonomous
nonlinear ordinary differential equations
Meromorphic exact solutions of the generalized Bretherton equation
The generalized Bretherton equation is studied. The classification of the
meromorphic traveling wave solutions for this equation is presented. All
possible exact solutions of the generalized Brethenton equation are given
Influence of Rashba and Dresselhaus spin-orbit interactions of equal strengths on electron states in a circular quantum ring in the presence of a magnetic field
Solutions of the Schr\"odinger equation are obtained for an electron in a
two-dimensional circular semiconductor quantum ring in the presence of both
external uniform constant magnetic field and the Rashba and Dresselhaus
spin-orbit interactions of equal strengths. Confinement is simulated by a
realistic potential well of a finite depth. The dependence of the energy levels
on a magnetic field strength, strength of spin-orbit interaction and a relative
ring width is presented.Comment: 6 pages, 2 figures, 1 tabl
Rashba spin-orbit interaction in a circular quantum ring in the presence of a magnetic field
Exact wave functions and energy levels are obtained for an electron in a
two-dimensional semiconductor circular quantum ring with a confining potential
of finite depth in the presence of both an external magnetic field and the
Rashba spin-orbit interaction.Comment: 7 pages, 4 figures, 2 table
Relations for zeros of special polynomials associated to the Painleve equations
A method for finding relations for the roots of polynomials is presented. Our
approach allows us to get a number of relations for the zeros of the classical
polynomials and for the roots of special polynomials associated with rational
solutions of the Painleve equations. We apply the method to obtain the
relations for the zeros of several polynomials. They are: the Laguerre
polynomials, the Yablonskii - Vorob'ev polynomials, the Umemura polynomials,
the Ohyama polynomials, the generalized Okamoto polynomials, and the
generalized Hermite polynomials. All the relations found can be considered as
analogues of generalized Stieltjes relations.Comment: 17 pages, 5 figure
Explicit summation of the constituent WKB series and new approximate wave functions
The independent solutions of the one-dimensional Schr\"odinger equation are
approximated by means of the explicit summation of the leading constituent WKB
series. The continuous matching of the particular solutions gives the uniformly
valid analytical approximation to the wave functions. A detailed numerical
verification of the proposed approximation is performed for some exactly
solvable problems arising from different kinds of potentials.Comment: 8 pages, LaTeX, minor changes and stylistic improvements, final
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