SEARCH FOR HIGH-DIMENSIONAL INTEGRABLE MODELS

The possible high dimensional integrable models are studied in three d ifferent aspects: (i) starting from a strong symmetry operator of a kn own (1 + 1)-dimensional integrable model, we can construct a type of ( n + 1)-dimensional integrable models, high dimensional breaking solito n equations; (ii)from every concrete realization of the generalized Vi rasoro algebra, we can get many high dimensional integrable models in the meaning that the models possess generalized Virasoro symmetry alge bra; (iii)starting from the Schwartz equations which possess conformal invariance, we can also get various high dimensional integrable model s in the meaning that they possess Painleve property.