Results 31 to 40 of about 549 (46)

Enhanced HBVMs for the numerical solution of Hamiltonian problems with multiple invariants

, 2013
Recently, the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficient solution of Hamiltonian problems, as well as for other types of conservative problems.
Brugnano, Luigi, Sun, Yajuan
core   +1 more source

Effective-mass Schroedinger equation and generation of solvable potentials

, 2004
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra.
Bagchi, B., Gorain, P., Quesne, C., Roychoudhury, R.   +3 more
core   +1 more source

Perturbed Poeschl-Teller oscillators

, 2000
Wave functions and energies are constructed in a short-range Poeschl-Teller well (= negative quadratic secans hyperbolicus) with a quartic perturbation. Within the framework of an innovated, Lanczos-inspired perturbation theory we show that our choice of
Cooper, Hautot, Lanczos, Miloslav Znojil, Pöschl, Skála, Tater, Znojil, Znojil, Znojil   +9 more
core   +2 more sources

Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation

, 2002
It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function.
Andrianov, Andrianov, Andrianov, Andrianov, Andrianov, Andrianov, Andrianov, Aoyama, Aoyama, Aoyama, Bandle, Calogero, Cannata, Cooper, Crum, Darboux, Eliezer, Ermakov, Espinoza, H.J Korsch, Hone, Junker, Klishevich, Korsch, Lewis, Lewis, M.V Ioffe, Matveev, Milne, Pinney, Plyushchay, Rogers, Sasaki, Thylwe, Thylwe, Turbiner, Ushveridze   +36 more
core   +1 more source

Deformation of a renormalization-group equation applied to infinite-order phase transitions

, 2003
By adding a linear term to a renormalization-group equation in a system exhibiting infinite-order phase transitions, asymptotic behavior of running coupling constants is derived in an algebraic manner.
C. Itoi, C. Itoi, H. Hamidian, Hisamitsu Mukaida, J. Bricmont, J. Bricmont, J. Wirstam, J.M. Kosterlitz, K.G. Wilson, L. Peliti, L.-Y. Chen, V.L. Berezinskiǐ, X. Xing   +12 more
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Minimal Length Uncertainty Relations and New Shape Invariant Models

, 2007
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation.
Donald Spector, Gendenshtein L. E.
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On the principal bifurcation branch of a third order nonlinear long-wave equation

, 2005
We study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long--wavelength instability. We show that the main bifurcation branch can be derived from a variational principle.
Benguria R D, Benguria R D, Chapman C J, Cox S M, Depassier M C, Doedel E J, Gertsberg V L, Hurle D T J, M C Depassier, Nepomnyashchy A A, Novick-Cohen A, Oron A, Oron A, R D Benguria, Riley D S, Sarocka D C, Scriven L E, Sivashinsky G I, Smith K A, Takashima M   +19 more
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Analytic solutions of the geodesic equation in axially symmetric space-times

, 2009
The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented.
Hackmann, E., Kagramanova, V., Kunz, J., Lämmerzahl, C.   +3 more
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Incomplete beta-function expansions of the solutions to the confluent Heun equation

, 2009
Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is introduced.
Abramowitz M, Artur Ishkhanyan, Baber W G, Cheb-Terrab E S, Darboux G, Erdélyi A, Erdélyi A, Ishkhanyan A M, Ishkhanyan A M, Ronveaux A, Slavyanov S Yu   +10 more
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Learning by Population Genetics and Matrix Riccati Equation. [PDF]

Entropy (Basel), 2023
Kozyrev S.
europepmc   +1 more source