Published April 2001 | Version v1
Journal article Metadata-only

Symmetry of the hyperbolic systems of the Riccati equation type

Creators

  • 1. Sterlitamakskij Gosudarstvennyj Pedagogicheskij Inst., Sterlitamak (Russian Federation)

Description

The Riccati equations are proved to have two hierarchies of symmetries linked by gauge transformation. In particular, in case of A1(1) algebra one derives the Konno equation and the appropriate hierarchies of symmetries contain the Schroedinger nonlinear equation and the Heisenberg equation of a magnetic substance

Abstract (Russian)

Доказано, что уравнения Риккати имеют две иерархии симметрий, связанные калибровочным преобразованием. В частности, в случае алгебры A1(1) получается известное уравнение Конно, и соответствующие иерархии симметрий содержат нелинейное уравнение Шредингера и уравнение магнетика Гейзенберга

Additional details

Additional titles

Original title (Russian)
Симметрии гиперболических систем типа уравнения Риккати

Publishing Information

Journal Title
Teoreticheskaya i Matematicheskaya Fizika
Journal Volume
127
Journal Issue
1
Journal Page Range
p. 47-62
ISSN
0564-6162
CODEN
TMFZAL

INIS

Country of Publication
Russian Federation
Country of Input or Organization
Russian Federation
INIS RN
33021237
Subject category
S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI
GAUGE INVARIANCE; HEISENBERG MODEL; NONLINEAR PROBLEMS; RICCATI EQUATION; SCHROEDINGER EQUATION; SYMMETRY
Descriptors DEC
CRYSTAL MODELS; DIFFERENTIAL EQUATIONS; EQUATIONS; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS

Optional Information

Notes
12 refs.