In this paper we consider the problem of constructing solutions of sev
eral well known nonlinear partial differential equations (p.d.e.s) in
phase space (i.e. the Fourier transform domain). We seek solutions rep
resenting travelling focussed pulses. As such, based on a technique us
ed to construct such solutions (so called Localized Wave solutions) of
linear p.d.e.s, we look for phase space solutions consisting of a gen
eralized function whose support is a particular line or surface, toget
her with a suitable weighting function. The support of the phase space
solution must be such that it regenerates itself after the appropriat
e nonlinear operation. In one spatial dimension we construct the usual
well known soliton solutions of several equations. For the case of hi
gher spatial dimensions we construct a travelling ''slab'' pulse solut
ion of the nonlinear Schrodinger equation. We also discuss some issues
involved with the extra freedom one has for the phase space support,
leading perhaps to more exotic spacetime domain solutions.