Vortex Method for Integrating Hamilton Equations

Abstract

As is known (see Sec. 7 in Chap. 1), the Hamilton—Jacobi method reduces the problem of solving the canonical equations

$${\dot x_i} = \frac{{\partial H}}{{\partial {y_i}}},{\dot y_i} = - \frac{{\partial H}}{{\partial {x_i}}},1in$$

(1.1)

where H = H(x, y, t), to investigating the first-order partial differential equation

$$\frac{{\partial S}}{{\partial t}} + H\left( {{x_1}, \ldots {x_n},\frac{{\partial S}}{{\partial {x_1}}}, \ldots ,\frac{{\partial S}}{{\partial {x_n}}},t} \right) = 0$$

(1.2)

.