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arXiv · 1703.05277

The derivative NLS equation: global existence with solitons

Yusuke Shimabukuro·Aaron Saalmann·Dmitry E. Pelinovsky
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Abstract

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 B\"acklund 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.

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Yusuke Shimabukuro, Aaron Saalmann, Dmitry E. Pelinovsky. 2017-03-15. The derivative NLS equation: global existence with solitons. https://arxiv.org/abs/1703.05277

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