The Solvability of the Initial-Boundary Value Problems for a Nonlinear Schrödinger Equation with a Special Gradient Term

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.

Mathematics Subject Classification 2010: 35D, 35M, 35Q.
Key words: Schrödinger equation, special gradient term, existence and uniqueness, first and second initial-boundary value problems.

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