LONG-TIME ASYMPTOTIC BEHAVIOR OF THE SOLUTION TO THE COUPLED HIROTA EQUATIONS WITH DECAYING INITIAL DATA

摘要

We consider the long-time asymptotic behavior for the Cauchy problem of the integrable coupled Hirota equations with 3x3 matrix spectral problem on the line with the initial value belonging to the Schwartz space. The precise asymptotic formulas and uniform error estimates are presented based on the nonlinear steepest descent analysis of an associated matrix Riemann-Hilbert problem.