A new family of partially coherent pulsed beams with spatial cosine-Gaussian and temporal Laguerre–Gaussian correlations, named spatial cosine-Gaussian and temporal Laguerre–Gaussian correlated Schell-model (SCTLGSM) pulsed beams, is introduced. An analytic propagation formula is derived for the SCTLGSM pulsed beam through the spatiotemporal ABCD optical system characterizing a continuous dispersive medium. As an example, the evolution of spatiotemporal intensity of the SCTLGSM pulsed beam in a

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... still, pure water column is then investigated. It is found that the SCTLGSM pulsed beams simultaneously exhibit spatiotemporal self-splitting and self-focusing phenomena, which can be attributed to the special spatial/temporal coherence structures and the presence of pulse chirper in the source plane. The physical interpretation of the obtained phenomena is given. The results obtained in this paper will be of interest in underwater optical technologies, e.g., directed energy and communications.