English

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

Exactly Solvable and Integrable Systems 2023-12-13 v1

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.

Keywords

Cite

@article{arxiv.2312.07185,
  title  = {The coupled hirota equation with a 3*3 lax pair: painleve-type asymptotics in transition zone},
  author = {Xao-Dan Zhao and Lei Wang},
  journal= {arXiv preprint arXiv:2312.07185},
  year   = {2023}
}