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Three classes of nonlinear integral equations and first order integrodifferential equations in two variables are dealt with where the quadratic nonlinearity is given by the correlation-convolution integral. In the case of the quarter plane the equations are reduced to boundary value problems for holomorphic functions which can be solved in closed form. In this way existence and constructive formulas for the solutions to the equations are derived.doi:10.4171/zaa/1201 fatcat:52esgucj5vhx3ne5auays4t4om