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

We consider the Painleve asymptotics for a solution of integrable coupled Hirota equationwith a 33 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 33 matrix Riemann-Hilbert problem.