  The existence, stability and other dynamical properties of a new type of
multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional
(1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger
equation with the self-defocusing cubic nonlinearity are studied. The equation
describes propagation of light in a medium with normal group-velocity
dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its
spectrum does not support a true bandgap. Nevertheless, the variational
approximation (VA) and numerical computations reveal stable solutions that seem
as completely localized ones, an explanation to which is given. The solutions
are of the gap-soliton type in the transverse direction(s), in which the
periodic potential acts in combination with the diffraction and self-defocusing
nonlinearity. Simultaneously, in the longitudinal (temporal) direction these
are ordinary solitons, supported by the balance of the normal GVD and
defocusing nonlinearity. Stability of the solitons is predicted by the VA, and
corroborated by direct simulations.
