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 Char P.
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 distributions are locally finite.
A nonlinear equation in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.
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