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