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In physics, Droplet-shaped waves are casual localized solutions of the wave equation closely related to the X-shaped waves, but, in contrast, possessing a finite support. A family of the droplet-shaped waves was obtained by extension of the "toy model" of X-wave generation by a superluminal point electric charge (tachyon) at infinite rectilinear motion 〔E. Recami, M. Zamboni-Rached and C. Dartora, (Localized X-shaped field generated by a superluminal electric charge. ) ''Physical Review E'' 69(2), 027602 (2004), doi:10.1103/PhysRevE.69.027602 〕 to the case of a line source pulse started at time . The pulse front is supposed to propagate with a constant superluminal velocity (here is the speed of light, so ). In the cylindrical spacetime coordinate system , originated in the point of pulse generation and oriented along the (given) line of source propagation (direction ''z''), the general expression for such a source pulse takes the form : where and are, correspondingly, the Dirac delta and Heaviside step functions while is an arbitrary continuous function representing the pulse shape. Notably, for , so for as well. As far as the wave source does not exist prior to the moment , a one-time application of the causality principle implies zero wavefunction for negative values of time. As a consequence, is uniquely defined by the problem for the wave equation with the time-asymmetric homogeneous initial condition : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Droplet-shaped wave」の詳細全文を読む スポンサード リンク
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