785 research outputs found

    Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations

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    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

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    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

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    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

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    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

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    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

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    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 versio
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