  The derivation of nonlinear integrable evolution partial differential
equations in higher dimensions has always been the holy grail in the field of
integrability. The well-known modified KdV equation is a prototypical example
of integrable evolution equations in one spatial dimension. Do there exist
integrable analogs of modified KdV equation in higher spatial dimensions? In
what follows, we present a positive answer to this question. In particular,
rewriting the (1+1)-dimensional integrable modified KdV equation in
conservation forms and adding deformation mappings during the process allow one
to construct higher dimensional integrable equations. Further, we illustrate
this idea with examples from the modified KdV hierarchy, also present the Lax
pairs of these higher dimensional integrable evolution equations.
