U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3430566· OSTI ID:21362148

Zheltukhin, A A ^[1]; Trzetrzelewski, M ^[2]

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1. Kharkov Institute of Physics and Technology, 1, Akademicheskaya St., Kharkov 61108 (Ukraine)
2. M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow (Poland)

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

• OSTI ID: 21362148
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 6; Other Information: DOI: 10.1063/1.3430566; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EXACT SOLUTIONS
GEOMETRY
MINKOWSKI SPACE
M-THEORY
NONLINEAR PROBLEMS
SPACE-TIME
TIME DEPENDENCE
U-1 GROUPS
UNITARY SYMMETRY
VECTORS
EQUATIONS
LIE GROUPS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MATHEMATICS
SPACE
SYMMETRY
SYMMETRY GROUPS
TENSORS
U GROUPS