The Hamilton-Jacobi Equations for Strings and p-Branes

Simple derivation of the Hamilton-Jacobi equation for bosonic strings and p-branes is given. The motion of classical strings and p-branes is described by two and p+1 local fields, respectively. A variety of local field equations which reduce to the Hamilton-Jacobi equation in the classical limit are given. They are essentially nonlinear, having no linear term.