Systematic method for solving strings having a symmetry in the space-time

In the presence of certain symmetry, called cohomogeneity-one symmetry, the equation of motion of an extended object in spacetime reduces to the problem of finding geodesics on a certain orbit space. We present a general method for obtaining solutions of such extented objects and classifying them. The classification is carried out in 4-dimensional Minkowski space and in 5-dimensional anti-de Sitter space. The solvability condition is described in terms of Killing vectors and Killing tensors which mutually commute. In 4-dimensional Minkowski space, it is found that all types of cohomogeneity-one strings are solvable. In the case of 5-dimensional de Sitter space, there are not enough number of commuting Killing vectors but that the problem reduces to that of finding curves on a two-dimensional surface.