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

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

2009-05-13

arxiv.org/abs/0905.2095v3

J.Math.Phys.51:1,2010

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, v3 published version

Scientific paper

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.

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