.png){kind=icon}
.png){kind=icon}
Return
CONTROLLABILITY OF THE FOURTH-ORDER SCHRÓDINGER EQUATION WITH QUASI-LINEAR PERTURBATIONS
.png){kind=icon}
PRE
AI
F
Y
C
W
DOI：10.3934/cpaa.2026030.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, we investigate the exact controllability of the cubic fourth-order Schr & otilde;dinger equation with quasi-linear Hamiltonian perturbations, where the control acts on a subset of the circle. First, the associated linearized operator is conjugated to a time-dependent operator with variable coefficients, modulo a bounded remainder. The main difficulty arises from the presence of off-diagonal elements in the coefficient matrices of the lower-order terms and the coupling between the highest-order term's coefficient and those of the lower-order terms. To address this, we construct bounded and invertible transformations. Subsequently, we analyze the existence of a right inverse for the linearized operator by examining the corresponding linear control problem. Finally, by applying the Nash-Moser-H & otilde;rmander implicit function theorem, we establish the exact controllability of the fourth-order Schr & otilde;dinger equation under quasi-linear perturbations.
Keywords:
Exact controllability
fourth-order Schr & otilde
dinger equation
observability
quasi-linear perturbation
Nash-Moser-H & otilde
rmander implicit theorem
Journal
C
IF:
0.9
Papers:
88
Citations:
0
Organization
Cited Papers