A Riemann–Hilbert Approach to Complex Sharma–Tasso–Olver Equation on Half Line

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver （cSTO） equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a（λ）, b（A）} and {A（λ）, B（λ）}, which depending on initial data uo（ x ） = u（ x, 0） and boundary data go（y） = u（0, y）, gl（y） = us（0, y）, g2（y） = uxx（0, y）. These spectral functions are not independent, they satisfy a global relation.