AUTHOR=Barkov Ruslan , Shepelsky Dmitry 

TITLE=A Riemann–Hilbert approach to solution of the modified focusing complex short pulse equation

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 10 - 2024

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1466965

DOI=10.3389/fams.2024.1466965

ISSN=2297-4687

ABSTRACT=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.