The coupled hirota equation with a 3*3 lax pair: painleve-type asymptotics in transition zone

Author:

Xao-Dan Zhao, Lei Wang

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI)

journal:

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date:

2023-12-12 00:00:00

Abstract

We consider the Painleve asymptotics for a solution of integrable coupled Hirota equationwith a 3*3 Lax pair whose initial data decay rapidly at infinity. Using Riemann-Hilbert techniques and Deift-Zhou nonlinear steepest descent arguments, in a transition zone defined by /x/t-1/(12a)/t^2/3<=C, where C>0 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 Painleve II equation associated with a 3*3 matrix Riemann-Hilbert problem.