Abstract
AbstractIn this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy problem, both on the real line and on the circle, we apply the short-time Fourier restriction method to establish a priori estimate for small and smooth solutions in Sobolev spaces $H^{s}$
H
s
with $s>1/4$
s
>
1
/
4
.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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