On behavior analysis of solutions for the coupled higher-order WKI equation (Q6546004)

The authors solve the coupled higher-order Wadati-Konno-Ichikawa (WKI) equation by reduction to the vector-matrix Riemann-Hilbert (RH) problem. Using the inverse scattering transformation they first derive the \(4 \times 4\) matrix Lax pair. The RH problem is established by using the inverse scattering transformation. Resorting to the nonlinear steepest descent method, the solution of the basic RH problem is transformed to the solution of the model RH problem after several contour deformation. Finally, the authors explicitly obtain the long-time asymptotics of the solution to the Cauchy problem of the WKI equation in the solitonless sector region with the aid of the parabolic cylinder function.