This article concerns the solvability of the nonlinear Schrodinger equation with gauge invariant power nonlinear term in one space dimension. The well-posedness of this equation is known only for with . Under some assumptions on the nonlinearity, this paper shows that this equation is uniquely solvable for special but typical initial data, namely the linear combinations of and p.v. (1/x), which belongs to . The proof in this article allows -perturbations on the initial data.
Submitted March 27, 2015. Published November 10, 2015.
Math Subject Classifications: 35Q55.
Key Words: Nonlinear Schrodinger Equations; solvability; rough initial data.
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| Takeshi Wada |
Department of Mathematics
Matsue 690-8504, Japan
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