Abstract
We present a nonlinear Fourier transform pair in any number of dimensions. This pair cannot be expressed in closed form but is defined through the solution of certain linear integral equations. The derivation of this result is based on the formulation of a nonlocal d-bar problem. The above nonlinear Fourier transform pair can be used for the solution of the Cauchy problem of a large class of nonlinear evolution equations in any number of spatial dimensions. Unfortunately, these nonlinear equations are highly nonlocal. Nevertheless, for the case of two dimensions they do reduce to the Davey–Stewartson equation which is a prototypical example of an integrable nonlinear evolution partial differential equation.
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