This article is cited in 2 papers

The solvability of the initial-boundary value problems for a nonlinear Schrödinger equation with a special gradient term

G. Yagub^a, N. S. Ibrahimov^bc, M. Zengin<sup>a

a</sup> Kafkas University, Paşaçayırı Campus, Kars, 36040, Turkey
^b Baku State University, 23 Academic Zahid Khalilov St., Baku, AZ 1148, Azerbaijan
^c Lankaran State University, 50 Hazi Aslanov St., Lankaran, AZ 4200, Azerbaijan

Abstract: In this paper, the initial-boundary value problems for the two-dimensional nonlinear Schrödinger equation with a special gradient term with purely imaginary coefficients in the nonlinear part, when the coefficients of the equation are measurable bounded functions, are considered. The existence and uniqueness of solutions of the first and second initial-boundary value problems is proved almost everywhere.

Key words and phrases: Schrödinger equation, special gradient term, existence and uniqueness, first and second initial-boundary value problems.

MSC: 35D, 35M, 35Q

Received: 13.02.2017
Revised: 10.01.2018

Language: English

DOI: 10.15407/mag14.02.214