Theoretical consideration of the propagation of femtosecond Gaussian pulses in a one-dimensional composite medium, consisting of alternating self-focusing and self-defocusing waveguide segments with normal group-velocity dispersion, predicts the generation of trains of bright solitons when an optical pulse first propagates in the self-focusing segment, followed by the self-defocusing one. The multiple temporal compression process, based on this setting, offers a method for controllable generation of multiple ultrashort temporal solitons. Numerical solutions of the generalized nonlinear Schrödinger equation modeling this system demonstrate that the intrapulse Raman scattering plays a major role in the temporal and spectral dynamics. Collisions between ultrashort solitons with different central wavelengths are addressed too. The paper provides a procedure for producing controllable trains of ultrashort temporal solitons by incident optical pulses propagating in a composite medium.