A new Lie algebra and soliton solutions, Bachlund transformation of soliton equations

摘要

A new Lie algebra is introduced for which a soliton hierarchy of nonlinear evolution equations is derived from zero curvature equations. A reduced equation from the hierarchy is obtained whose exact solutions are produced. Again using the Lie algebra and the corresponding loop algebra, a type of nonlinear soliton equations with exponential terms in potential functions are given. The Backlund transformation among them is also generated.