Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 279, pp. 1-6.
Title: Solutions to nonlinear Schrodinger equations for special initial data
Author: Takeshi Wada (Shimane Univ., Matsue, Japan)
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
belong 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.