A new variant of the conditional symmetry method for obtaining
rank-k solutions of hydrodynamic-type systems in many dimensions
is presented. The main idea here is to select the supplementary
differential contraints, employed by this method, in such a way
that they ensure the existence of solutions expressible in terms
of Riemann invariants. These constraints prove to be less restrictive
than the conditions required by the generalized method of characteristics
and, as a result, one obtains larger classes of solutions. The proposed
approach is applied to the fluid dynamic equations in (3+1) dimensions.
Several new soliton-like solutions (among them kinks, bumps and multiple
wave solutions) are constructed.