The coupled Hirota equations with a 3×3$3\times 3$ Lax pair: Painlevé‐type asymptotics in transition zone

Abstract

AbstractWe consider the Painlevé asymptotics for a solution of the integrable coupled Hirota equations with a Lax pair whose initial data decay rapidly at infinity. Using the Riemann–Hilbert (RH) techniques and Deift–Zhou nonlinear steepest descent arguments, in a transition zone defined by , where is a constant, it turns out that the leading‐order term to the solution can be expressed in terms of the solution of a coupled Painlevé II equations, which are associated with a matrix RH problem and appear in a variety of random matrix models.