A Riemann–Hilbert approach to solution of the modified focusing complex short pulse equation - Barkov, Ruslan; Shepelsky, Dmitry (Frontiers in Applied Mathematics and Statistics, 2024)
We develop a Riemann--Hilbert approach to the modified focusing complex short pulse (mfcSP) equation \[ u_{xt}=u+\tfrac{1}{2}\bar u(u^2)_{xx} \] with zero boundary conditions (as $\abs{x}\to\infty$). We obtain a parametric representation of the solution of the initial value problem for the mfcSP equation in terms of the solution of the associated Riemann--Hilbert problem. This representation is then used for retrieving one-soliton solutions.