A Lie group framework for soliton equations. I. Path independent case

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Abstract
A general Lie group theoretic framework for the study of a class of nonlinear partial differential equations is presented. In two space–time dimensions this class includes soliton equations. The approach is applicable in N⩽2 space–time dimensions. Eigenvalue problems and isospectral flows associated with equations have a natural group theoretic interpretation in this framework. A sequence of nonlocal exact 1‐,2‐,...,(N−1) ‐forms are derived in N‐dimensional space–time.