INFINITELY MANY LAX PAIRS AND SYMMETRY CONSTRAINTS OF THE KP EQUATION

Starting from a known Lax pair, one can get some infinitely many coupl ed Lax pairs, infinitely many nonlocal symmetries and infinitely many new integrable models in some different ways. In this paper, taking th e well known Kadomtsev-Petviashvili (KP) equation as a special example , we show that infinitely many nonhomogeneous linear Lax pairs can be obtained by using infinitely many symmetries, differentiating the spec tral functions with respect to the inner parameters. Using a known Lax pair and the Darboux transformations (DT), infinitely many nonhomogen eous nonlinear Lax pairs can also be obtained. By means of the infinit ely many Lax pairs, DT and the conformal invariance of the Schwartz fo rm of the KP equation, infinitely many new nonlocal symmetries can be obtained naturally. Infinitely many integrable models in (1+1)-dimensi ons, (2+1)-dimensions, (3+1)-dimensions and even in higher dimensions can be obtained by virtue of symmetry constraints of the KP equation r elated to the infinitely many Lax pairs. (C) 1997 American Institute o f Physics.