Obtain high dimensional integrable models by means of Miura type noninvertible transformation

Searching for high dimensional integrable models (especially in 3 + 1 dimensions) is one of the most important problems in nonlinear physics. In this paper,we establish a method to find some high dimensional integrable models via some noninvertible deformation relations. A noninvertible deformation relation may not only transform an integrable model to a nonintegrable model,but also deform a nonintegrable model to an integrable model. Concretely,starting from a noninvertible Miura type transformation relation and the linear wave equation,we obtain a nontrivial high dimensional Painleve integrable model.