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The Kadomtsev–Petviashvili (KP) equation (ut+3uux/2+ 1/4 uxxx)x +3σuyy/4=0 allows an infinite-dimensional Lie group of symmetries, i.e., a group transforming solutions amongst each other. The Lie algebra of this symmetry group depends on three arbitrary functions of time ‘‘t’’ and is shown to be related to a subalgebra of the loop algebra A(1)4. Low-dimensional subalgebras of the symmetry algebra are identified, specifically all those of dimension n≤3, and also a physically important six-dimensional Lie algebra containing translations, dilations, Galilei transformations, and ‘‘quasirotations.’’ New solutions of the KP equation are obtained by symmetry reduction, using the one-dimensional subalgebras of the symmetry algebra. These solutions contain up to three arbitrary functions of t.

These findings provide support for the considerable variability in the trajectory of the development of PTSD and suggest that although ASD is associated with subsequent PTSD, the predictive role of initial reactions is limited.