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We represent an integration algorithm combining the characteristics methodand Hopf-Cole transformation. This algorithm allows one to partially integratea large class of multidimensional systems of nonlinear Partial DifferentialEquations (PDEs).  A specific generalization of the equation describing the dynamics oftwo-dimensional viscous fluid and a generalization of the Korteweg-de Vriesequation are examples of such systems. The richness of available solution spacefor derived nonlinear PDEs is discussed.

Partially integrable generalizations of classical integrable models by combination of characteristics method and Hopf-Cole transformation