Symmetry in Nonlinear Mathematical Physics - 2009

Jing Kang (Northwest University, Xi'an, P.R. China)

Hodograph-type transformations for linearization of systems of nonlinear diffusion equations

We study the problem of the linearization of a class of nonlinear systems of equations which is a potential form of a class of systems of nonlinear diffusion equations. We construct a class of point transformations of the form t' = t; x' = X(u,v); u' = R(x,u,v); v'= S(x,u,v) which can linearize the nonlinear systems. These point transformations are hodograph-type transformations which have the property that the new independent and dependent variables depend respectively on the old dependent and independent variables. All systems of equations admitting such transformations are completely classified.