The unified transform method to the high-order nonlinear Schrodinger equation with periodic initial condition

In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.