two questions concerning IST

Hello !

I've got two questions about inverse scattering transform (nonlinear
PDEs). If a certain equation
is integrable by IST method then it should be possible to solve it
analytically for any initial value problem (find scattering data,
evolve them and find a solution). Experience and some old papers sugest
that it is so fine only for multiple soliton solutions, but as it well
known these systems are integrable. The first question is: where to
find some example of this for non multisoliton data (arbitrary u(x,0))
and the second is why people are solving for example KdV using
numerical methods ? (I'm asking this question here because of the
discussion "Solitons in One Post"
which took place here some time ago)

allor47

.