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Is there any order for solving a set of nonlinear coupled partial differential equations analytically i.e. without a numerical algorithm.

I cant solve the following set of equations $$ \partial_xf_1(x,t) + a_1\partial_tf_1(x,t) + b_1\partial_{tt}f(x,t) = c_1f_3f_2\\ \partial_xf_2(x,t) + a_2\partial_tf_1(x,t) + b_2\partial_{tt}f(x,t) = c_2f_3f_1\\ \partial_xf_3(x,t) + a_3\partial_tf_1(x,t) + b_3\partial_{tt}f(x,t) = c_3f_1f_2 $$

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