U(1)-invariant membranes: The geometric formulation, Abel and pendelum differential equations
2010 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 062303, 062303-1-062303-12 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 51, no 062303, 062303-1-062303-12 p.
IdentifiersURN: urn:nbn:se:su:diva-40395DOI: 10.1063/1.3430566ISI: 000279993400010OAI: oai:DiVA.org:su-40395DiVA: diva2:323763