Energy minimality property of the connecting solution of the Painlevé phase transition model

2019/05/13 by Sourdis, C.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.04846

Abstract

We establish the energy minimality property of solutions to the generalized Painlevé-II equation Δy-x₁y-2y³=0, (x₁,x₂)∈ ℝ², which are increasing in x₂ and converge to the positive and negative Hastings-McLeod solutions as x₂→ ± ∞.

Related

• The connecting solution of the Painlevé phase transition model
• A phase transition for non-intersecting Brownian motions, and the Painleve II equation
• Vortex solutions in the Ginzburg-Landau-Painlevé theory of phase transition
• Connection problem of the first Painlevé transcendent between poles and negative infinity
• Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation