Asymptotics and total integrals of the ${\mathrm{P}}_{\mathrm{I}}^2$ tritronquée solution and its Hamiltonian

Dan Dai, Wen-Gao Long

We study the tritronquée solution $u(x,t)$ of the ${\mathrm{P}}_{\mathrm{I}}^2$ equation, the second member of the Painlevé I hierarchy. This solution is pole-free on the real line and…