Hybrid Ermakov-Painlevé IV Systems
نویسندگان
چکیده
Ermakov-Painleve IV coupled systems are introduced and associated Ermakov-type invariants isolated. These used to obtain systematic reduction of the system in terms canonical Painleve equation. The procedure is applied a symmetry derivative resonant nonlinear Schro dinger triad incorporating de Broglie-Bohm potential terms.
منابع مشابه
Lie Point Symmetries for Reduced Ermakov Systems
Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2, R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of ...
متن کاملGeneralized Hamiltonian Structures for Ermakov Systems
We construct Poisson structures for Ermakov systems, using the Er-makov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations...
متن کاملFour - Dimensional Painlevé Systems of Types
We find and study a five-parameter family of four-dimensional coupled Painlevé V systems with affine Weyl group symmetry of type D (1) 5 . We then give an explicit description of a confluence from those systems to a four-parameter family of four-dimensional coupled Painlevé III systems with affine Weyl group symmetry of type B (1) 4 . 0. Introduction It is well-known that the Painlevé systems P...
متن کاملOn Discrete Painlevé Equations Associated with the Lattice Kdv Systems and the Painlevé Vi Equation
1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP (generalised discrete Painlevé equation) ...
متن کاملPainlevé test and the first Painlevé hierarchy
Starting from the first Painlevé equation, Painlevé type equations of higher order are obtained by using the singular point analysis.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2021
ISSN: ['1776-0852', '1402-9251']
DOI: https://doi.org/10.1080/14029251.2014.975531