Y. Shimabukuro, A. Saalmann, and D.E. Pelinovsky
The derivative NLS equation: global existence with solitons
We extend the global existence result for the derivative NLS equation to the case when the
initial datum includes a finite number of solitons. This is achieved by an application of the Backlund
transformation that removes a finite number of zeros of the scattering coefficient. By means of this
transformation, the Riemann–Hilbert problem for meromorphic functions can be formulated as the one
for analytic functions, the solvability of which was obtained recently.
derivative NLS equation, global existence, inverse scattering transform, Backlund transformation