Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 279, pp. 16.
Solutions to nonlinear Schrodinger equations for special initial data
Takeshi Wada
Abstract:
This article concerns the solvability of the nonlinear Schrodinger
equation with gauge invariant power nonlinear term in one space dimension.
The wellposedness 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
Shimane University
Matsue 6908504, Japan
email: wada@riko.shimaneu.ac.jp

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