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We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
We study the microlocal analyticity of solutions of the nonlinear equationwhere 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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