Abstract
A coupled higher-order WKI equation is proposed and its 4 × 4 matrix Lax pair is derived. On the basis of spectral analysis of the 4 × 4 matrix spectral problems related to the coupled higher-order WKI equation, the basic Riemann–Hilbert problem is established by using the inverse scattering transformation. Resorting to the nonlinear steepest descent method, the solution of the basic Riemann–Hilbert problem is transformed to the solution of the model Riemann–Hilbert problem after several contour deformation. Finally, we explicitly obtain the long-time asymptotics of the solution to the Cauchy problem of the coupled higher-order WKI equation in the solitonless sector region with the aid of the parabolic cylinder function.
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