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D.E. Pelinovsky and Y. Shimabukuro

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Global existence in the derivative NLS equation
with the inverse scattering transform method

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**Abstract:**

We address existence of global solutions of the derivative nonlinear Schrodinger (DNLS) equation
without the small-norm assumption. By using the inverse scattering transform method without eigenvalues and resonances,
we construct a unique global solution in H^{2} intersecting with H^{1,1},
which is also Lipschitz continuous with respect to the initial data. Compared to the existing literature
on the spectral problem for the DNLS equation, we transform the Riemann-Hilbert problem
in the complex plane to the jump on the real line.

**Keywords**:

derivative NLS equation, global existence, inverse scattering transform, Kaup-Newell spectral problem,
Riemann-Hilbert problem