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 uxt=u+12u¯(u2)xx with zero boundary conditions (as |x| → ∞). 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.