We consider a boundary integral approach to some nonlinear partial differential equations from fluid dynamics. The nonlinear equations are replaced by a sequence of linear equations, each of which is solved by the boundary element method. In order to avoid body integral contributions to the boundary integral equations, an approximate particular solution is first derived. This is achieved by replacing the body terms with an approximation for which there is a known solution. The present paper considers an approximation in terms of Gaussian distributions, a representation that has several desirable features.
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