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Addressed here is the occurrence of point singularities which owe to the fo-cusing of short or long waves,a phenomenon labeled dispersive blow-up.The context of this investigation is linear and nonlinear,strongly dispersive equations or systems of equa-tions.The present essay deals with linear and nonlinear Schr(o)dinger equations,a class of fractional order SchrSdinger equations and the linearized water wave equations,with and without surface tension.Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.