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We address the existence of global solutions to the initial value problem forthe integrable nonlocal derivative nonlinear Schr\"{o}dinger equation inweighted Sobolev space $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$. The key toprove this result is to establish a bijectivity between potential andreflection coefficient by using the inverse scattering transform method in theform of the Riemann-Hilbert problem.

Existence of global solutions for the nonlocal derivation nonlinear Schr\"{o}dinger equation by the inverse scattering transform method