Optimal bilinear control of the logarithmic Schrödinger equation

Abstract

We investigate the optimal bilinear control of the 3D logarithmic nonlinear Schrödinger equation arises from quantum physics. To overcome the difficulty caused by the absence of the Lipschitz continuity at the origin due to the logarithmic nonlinearity, we use an approximate scheme. By studying the approximate systems and passing to a limit, we finally get the minimizer of the original optimal control problem.

Sound Propagation in Cigar-Shaped Bose Liquids in the Thomas-Fermi Approximation: A Comparative Study between Gross-Pitaevskii and Logarithmic Models

“…Fruitful applications of the logarithmic models were found in various physical systems [21][22][23][24][25][26][27][28][29][30][31][32]. Extensive mathematical studies of logarithmically nonlinear systems were performed as well, to mention only very recent results [33][34][35][36][37][38][39][40][41].…”