Electron. J. Diff. Equ., Vol. 2015 (2015), No. 279, pp. 1-6.

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 well-posedness of this equation is known only for $H^s$ with $s\ge 0$. 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 $\delta(x)$ and p.v. (1/x), which belongs to $H^{-1/2-0}$. The proof in this article allows $L^2$-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 690-8504, Japan
email: wada@riko.shimane-u.ac.jp

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