Well-Posedness of the Nonhomogeneous Initial-Boundary Value Problem for the Coupled Hirota Equation

In this work, we address the nonhomogeneous initial-boundary value problem for the coupled Hirota equation posed on the finite interval 0,L. To investigate the well-posedness of this problem, we first adopt an appropriate transformation, namely the Laplace transform, which is tailored to the specific characteristics of the problem, and further obtain an explicit solution formula for the linear inhomogeneous coupled system. Subsequently, the local well-posedness of the original nonhomogeneous initial-boundary value problem in Xs,T×Xs,TXs,T=C(0,T;Hs(0,1))∩L2(0,T;Hs+1(0,1)) is rigorously established through the combination of this explicit formula, the contraction mapping principle and energy estimates.