Global structure of the general solution of the Chew–Low equations

The Chew–Low equations for static $p$-wave $\pi N$ scattering are considered. The formulation of these equations in the form of a system of three nonlinear first-order difference equations is used, the general solution of the equations depending on three arbitrary periodic functions. An approach is proposed for the global construction of the general solution; it is based on an expansion in powers of one of the arbitrary functions $C(w)$, which determines the structure of the invariant curve of the Chew–Low equations. It is shown that in each order in $C(w)$ the original nonlinear problem reduces to a linear problem. By solution of the latter, the general solution of the Chew–Low equations is found up to terms quadratic in $C(w)$.