Elbow scattering and inverse scattering applications to LKdV and KdV (Q2737828)

By the inverse problem method the author studies some aspects of the solution of the mixed problem for the Korteweg-de Vries equation \(V_t+V_{xxx}-6VV_x\) on the half-line \(x>0,\) under the initial condition \(V(x,0)=V_0(x)\) and the boundary conditions \(\frac{\partial^{k-1}V}{\partial x^{k-1}}|_{x=0}=V_k(t)\), \(k=1,2,3\). The algorithm for the solution of this mixed problem along with necessary and sufficient conditions of its solvability are given in \textit{G. Freiling} and \textit{A. V. Yurko} [Inverse Sturm-Liouville problems and their applications, NOVA Science Publishers, New York (2001)]; see also \textit{V. A. Yurko} [Inverse Problems 7, No. 5, 727-738 (1991; Zbl 0739.35072)] for similar results for the Boussinesq equation.