Integrable non-isospectral flows associated with the Kadomtsev-Petviashvili equations in 2+1 dimensions

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Abstract
The symmetries of the Kadomtsev-Petviashvili (KP) equations in 2+1 dimensions yield two hierarchies of integrable non-linear evolution equations (NEE): one is the familiar family of isospectral flows-the KP hierarchy. The other is non-isospectral and its flows have coefficients which depend linearly on x and y. The spectral methods used to solve KP can be used to solve all these NEE. An underlying infinite-dimensional Lie algebra is used to determine all the Lax pairs for both families, and it also determines their symplectic structures. Constants of the motion are constructed for the non-isospectral cases.