Abstract
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 an integrable evolution equation in one spatial dimension. Do there exist integrable analogs of the 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 allows one to construct higher-dimensional integrable equations. Further, we illustrate this idea with examples from the modified KdV hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.
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