Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applicat...Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applications in physics lead to mathematical models where boundary data is inhomogeneous, e.g. in radio frequency wave experiments. In this paper, we investigate the mixed initial-boundary condition problem for the nonlinear Schrödinger equation iu<sub>t</sub> = u<sub>xx</sub> – g|u|<sup>p-1</sup>u, g ∈R, p > 3 on a semi-infinite strip. The equation satisfies an initial condition and Dirichlet boundary conditions. We utilize semi-group theory to prove existence and uniqueness theorem of a strong local solution.展开更多
文摘Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applications in physics lead to mathematical models where boundary data is inhomogeneous, e.g. in radio frequency wave experiments. In this paper, we investigate the mixed initial-boundary condition problem for the nonlinear Schrödinger equation iu<sub>t</sub> = u<sub>xx</sub> – g|u|<sup>p-1</sup>u, g ∈R, p > 3 on a semi-infinite strip. The equation satisfies an initial condition and Dirichlet boundary conditions. We utilize semi-group theory to prove existence and uniqueness theorem of a strong local solution.
