It is shown that the symmetry algebra of the Kadomtsev-Petviashvili equation can be related to an infinite-dimensional subalgebra of the loop algebra [$\mathrm{SL}(5, R)\otimes R(t, t^{-1\mathrm{}})\oplus \left[R\right(t, t^{-1\mathrm{}}\left)\frac{d}{\mathrm{dt}}\right]$. The algebra is used to generate new classes of solutions of the Kadomtsev-Petviashvili equation, depending on several arbitrary functions.

• Received 29 July 1985

DOI:https://doi.org/10.1103/PhysRevLett.55.2111