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A transformation domain description for nonlinear partial differential equations

Transfer function models for the description of physical systems with distributed parameters have recently been introduced to the field of multidimensional digital signal processing. They are an extension of the transfer functions description for one-dimensional systems and provide an alternative to the conventional representation by partial differential equations. Transfer function models are the starting point for the development of efficient discrete algorithms that are suitable for computer implementation. This paper extends the presented transformation domain description to nonlinear systems. A suitable choice of the integral transformations for the independent variables allows to treat certain types of nonlinearities in a similar way as for linear multidimensional systems.