To unintegrable function for the nonlinear dynamic equations of pulsed beams in six dimensional phase spaces

first of all

the integrated functions of the equations are expanded as Taylor series in independent variable

the general series solution of the independent variable for the equation can be obtained by direct integration.Then the coefficients for different order items of independent variable can be expanded as Taylor series in initial value

next series solution of the independent variable and initial value for the equation can be obtained.In order to solve the dynamic equation for relative motion of any particle to reference particle

first of all expanding the integrated function as Taylor series in independent variable

then the coefficients for difference order items of independent variable can be expanded as the series of reference particle initial value

the relative motion equation can be obtained

and series solution for the independent variable and relative motion initial value of the equation can be obtained by direct integration.