We study an inverse problem related to the dynamical Schrödinger equation in a bounded domain of R n , n ≥ 2. Since the concerned non-linear Schrödinger equation possesses a trivial solution, we linearize the equation around the trivial solution. Demonstrating the well-posedness of the direct problem under appropriate conditions on initial and boundary data, it is observed that the solution admits ε-expansion. By taking into account the fact that the terms O(|∇u(t, x)| 3 ) are negligible in this context, we shall reconstruct the time-dependent coefficients such as electric potential and vectorvalued function associated with quadratic nonlinearity from the knowledge of input-output map using the geometric optics solution and Fourier inversion. H r,s (Σ) = L 2 (0, T ; H r (∂Ω)) ∩ H s (0, T ; L 2 (∂Ω))2020 Mathematics Subject Classification. 35R30.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.