Results 21 to 30 of about 16,850 (158)

Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory [PDF]

, 2018
In this paper we start with proving that the Schr\"odinger equation (SE) with the classical $12-6$ Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Galois theory (DGT), for any value of energy; i.e., there are no solutions ...
Acosta-Humánez, Manuel F., Acosta-Humánez, Primitivo B., Tuirán, Erick   +2 more
core   +3 more sources

Galois theory, functional Lindemann-Weierstrass, and Manin maps [PDF]

, 2015
We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations.
Bertrand, Daniel, Pillay, Anand
core   +3 more sources

Integrability of Stochastic Birth-Death processes via Differential Galois Theory [PDF]

, 2019
Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the ...
Acosta-Humanez, Primitivo B., Capitan, Jose A., Morales-Ruiz, Juan J.   +2 more
core   +2 more sources

Iterative $q$-Difference Galois Theory [PDF]

, 2008
Initially, the Galois theory of $q$-difference equations was built for $q$ unequal to a root of unity. This choice was made in order to avoid the increase of the field of constants to a transcendental field. Inspired by the work of B.H. Matzat and M. van
Hardouin, Charlotte
core   +4 more sources

General differential Galois theory [PDF]

Moscow University Mathematics Bulletin, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Variations for Some Painlev\'e Equations [PDF]

, 2019
This paper first discusses irreducibility of a Painlev\'e equation $P$. We explain how the Painlev\'e property is helpful for the computation of special classical and algebraic solutions.
Acosta-Humánez, Primitivo B., Top, Jaap, van der Put, Marius   +2 more
core   +2 more sources

Differential Galois Theory and Hopf Algebras for Lie Pseudogroups

Axioms
According to a clever but rarely quoted or acknowledged work of E. Vessiot that won the prize of the Académie des Sciences in 1904, “Differential Galois Theory” (DGT) has mainly to do with the study of “Principal Homogeneous Spaces” (PHSs) for finite ...
Jean-Francois Pommaret
doaj   +1 more source

Splitting fields and general differential Galois theory

, 2010
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations.
A. Pillay, B. Poizat, D. Marker, Dmitry V Trushin, E. R. Kolchin, M. F. Atiyah, M. Rosenlicht, M. van der Put, Ph. J. Cassidy   +8 more
core   +1 more source

Reduced group schemes as iterative differential Galois groups

, 2019
This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative differential field ...
Maurischat, Andreas
core   +1 more source

Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations

Symmetry, Integrability and Geometry: Methods and Applications, 2012
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the ''invariance'' of the objects of the ''Darboux theory of integrability''. In particular,
Primitivo B. Acosta-Humánez, Chara Pantazi   +1 more
doaj   +1 more source