Solution of Chew–Low equations in the quadratic approximation

The second-order power contributions are found in the framework of the iterative scheme of construction of the general Chew–Low equation [1] proposed by Gerdt [2]. In contrast to the linear approximation obtained by Gerdt, the quadratic approximation has an infinite number of poles in the complex plane of the uniformizing variable $w$. It is shown that allowance for the quadratic corrections in the general solution makes it possible to distinguish the class of solutions possessing the required Born pole at the point $w=0$. The most cumbersome part of the analytic computations in the present study was done on a computer using the algebraic system REDUCE-2.