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We study the microlocal analyticity of solutions of the nonlinear equation
where is complex-valued, real analytic in all its arguments and holomorphic in . We show that if the function is a solution, and or if is a solution, , , and , then . Here denotes the analytic wave-front set of and Char is the characteristic set of the linearized operator. When , we prove a more general result involving the repeated brackets of and of any order.
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