  We suggest a method for calculation of parameters of dispersive shock waves
in framework of Whitham modulation theory applied to non-integrable wave
equations with a wide class of initial conditions corresponding to propagation
of a pulse into a medium at rest. The method is based on universal
applicability of Whitham's `number of waves conservation law' as well as on the
conjecture of applicability of its soliton counterpart to the above mentioned
class of initial conditions which is substantiated by comparison with similar
situations in the case of completely integrable wave equations. This allows one
to calculate the limiting characteristic velocities of the Whitham modulation
equations at the boundary with the smooth part of the pulse whose evolution
obeys the dispersionless approximation equations. We show that explicit
analytic expressions can be obtained for laws of motion of the edges. The
validity of the method is confirmed by its application to similar situations
described by the integrable Korteweg-de Vries (KdV) and nonlinear
Schr\"{o}dinger (NLS) equations and by comparison with the results of numerical
simulations for the generalized KdV and NLS equations.
