2 research outputs found
Riemann-Hilbert approach for the integrable nonlocal nonlinear Schr\"odinger equation with step-like initial data
We study the Cauchy problem for
the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation
with a step-like initial data: as and as , where is an arbitrary constant. We develop the inverse scattering transform method for this problem in the
form of the Riemann-Hilbert approach and obtain the representation of the solution of the Cauchy
problem in terms of the solution of an associated Riemann-Hilbert-type analytic factorization problem,
which can be efficiently used for further studying the properties of the solution, including the large time
asymptotic behavior