Non-Homogeneous Initial-Boundary Value Problem for Coupled Hirota Equation on the Half Line

We study the initial-boundary value problem of the coupled Hirota equation on the right half line with nonhomogeneous data. It is shown that the initial-boundary value problem is local well-posed. The main idea of the proof for the local well-posedness is to derive an explicit solution formula, which is obtained by applying the Fourier and Laplace transforms, and then obtain a priori estimates using the restricted norm method. Additionally, we obtain the smoothing results that the nonlinearities of the coupled Hirota equation on the half line are smoother than the initial data.