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- Title
On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions.
- Authors
Tin, Phan Van
- Abstract
In this paper we consider the Schrödinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We obtain the local well posedness for the Cauchy problem on Zhidkov spaces X k (R) X k (R) and in ϕ + H k (R) ϕ + H k (R). Moreover, we prove the existence of conservation laws by using localizing functions. Finally, we give explicit formulas for stationary solutions on Zhidkov spaces.
- Subjects
NONLINEAR Schrodinger equation; NONLINEAR equations; K-spaces; SCHRODINGER equation; CONSERVATION laws (Mathematics); COMMERCIAL space ventures; CONSERVATION laws (Physics); CAUCHY problem
- Publication
Evolution Equations & Control Theory, 2022, Vol 11, Issue 3, p837
- ISSN
2163-2472
- Publication type
Article
- DOI
10.3934/eect.2021028