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A nonlinear equation P (D)u = αu in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of CharP , one gets the… (More)
A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set… (More)
We consider a nonlinear Laplace equationu = f(x,u) in two variables. Following the methods of B. Braaksma (Br) and J. Ecalle used for some nonlinear ordinary differential equations we construct first… (More)
A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these… (More)