Solution of a nonlinear singular integral equation with quadratic nonlinearity - Gun’ko, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation$$u^2 \left( t \right) + \left( {\frac{1}{π }\int\limits_{ - ∞ }^∞ {\frac{{u\left( τ \right)}}{{τ - t}}dτ } } \right)^2 = A^2 \left( t \right)$$and determine the general form of a solution by using zeros of an entire function $A^2 (z)$ of exponential type.