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

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.Comment: 19 pages, v3 published versio

Junctions and the Fate of Branes in External Fields

We discuss the processes of brane bubble nucleation induced by the external branes. The quasiclassical solution for the nucleation by the single external brane has been found in the case when the brane junctions are possible. Exponential factor in the production rate has been calculated. The process induced by the fundamental or D string in the background of two D3 branes is analyzed and its interpretation from the D3 worldvolume theory viewpoint is described.Comment: 20 pages, Latex, version published in Nucl. Phy