Abstract

In this paper, we investigate the long-term asymptotic behavior of solutions to the Cauchy problem for the n-component coupled higher-order nonlinear Schrödinger (nC-HNLS) equation on a line with decaying initial data. Through the application of nonlinear steepest descent methods to an associated (n+1)×(n+1) matrix Riemann–Hilbert (RH) problem, we find that, within the sector defined by xt−13εt23⩽C, where C>0 is a constant, the asymptotics can be characterized in relation to the solution to a coupled modified Painlevé II equation. This relationship is connected to a corresponding (n+1)×(n+1) matrix RH problem.

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