Boutroux ansatz for the degenerate third Painlev\'e transcendents

Abstract

For a general solution of the degenerate third Painlev\'e equation we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips along generic directions. The expression is obtained by using isomonodromy deformation of a linear system governed by the degenerate third Painlev\'e equation.