{"ID":2824787,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22512","arxiv_id":"2512.22512","title":"Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control","abstract":"In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis on the control operator, we show the small-time global controllability of the CGL equation. The proof is obtained by developing a multiplicative version of a geometric control approach, introduced by Agrachev and Sarychev in \\cite{AS05,AS06}.","short_abstract":"In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis on the control operator, we show the small-time global controllability of the CGL...","url_abs":"https://arxiv.org/abs/2512.22512","url_pdf":"https://arxiv.org/pdf/2512.22512v1","authors":"[\"Xingwu Zeng\",\"Can Zhang\"]","published":"2025-12-27T08:00:24Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AP\"]","methods":"[]","has_code":false}