Multidimensional Laplace transforms for solution of nonlinear equations

Abstract

Nonlinear multivariable differential or integrodifferential equations with terms of mixed dimensionality can be solved using multidimensional transforms. The method for two variables is presented, for which, by inspection of the original equation, an explicit solution can be written as a multidimensional Laplace transform. The inverse of the multidimensional transform is found by the method of association of the variables. Initial nonzero conditions have been taken into consideration, while obtaining the explicit solution as a Volterra-series expansion.