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I am studying the Von Karman equations system (A semi-linear elliptic system of two fourth-order partial differential equations with two independent spatial variables) and I want to solve this equation by means of homotopy analysis method (HAM). After applying homotopy in accordance with the articles published by Mr. Liao and a similar paper by Mr. Van Görder in 2012, these nonlinear differential equations have become infinitely linear differential equations. To solve these linear equations, Mr. Van Görder used Fourier's analysis , but I do not know how many sentences to use from this series? Mr. Liao has also solved these equations using a wavelet. Also, my question is that to solve these equations, one can help to get an explicit and analytical expression?

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