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

Author:

Zhao Xiaodan1,Wang Lei2ORCID

Affiliation:

1. School of Control and Computer Engineering North China Electric Power University Beijing P. R. China

2. School of Mathematics and Physics North China Electric Power University Beijing P. R. China

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.

Funder

National Natural Science Foundation of China

Publisher

Wiley

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