Linearisable nonlinear partial differential equations in multidimensions

We show that the complexification of the independent variables of a given partial differential equation (PDE) provides a straightforward approach for both unifying certain large classes of PDEs, as well as generating new classes of linearisable PDEs in multidimensions. For example, by complexifying the Burgers equation, which is a linearisable PDE in 1 + 1, i.e., an evolution equation in one spatial dimension, it is possible to construct a linearisable PDE in N + 1, i.e., an evolution PDE in N > 1 spatial dimensions. Among these equations in 2 + 1 are certain linearisable PDEs which have been recently introduced in the literature.