Asymptotics of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation as $|x|\to\infty$

A complete asymptotic expansion as $x\to\pm\infty$ of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation $u_t+u_{xxx}+uu_x=0$ is constructed and validated. The expansion is infinitely differentiable in the variables $t$ and $x$ and, together with the asymptotic expansions of all its derivatives in independent variables, is uniform on any compact interval of variation of the time $t$.