We investigate a class of higher-order nonlinear dispersive equations posed
on the circle, subject to additive forcing by a finite-dimensional control. Our
main objective is to establish approximate controllability by using the
controllability of the inviscid Burgers system, linearized around a suitably
constructed trajectory. In contrast to earlier approaches based on Lie
algebraic techniques, our method offers a more concise proof and sheds new
light on the structure of the control. Although the approach necessitates a
higher-dimensional control space, both the structure and dimension of the
control remain uniform with respect to the order of the dispersive equation and
the control time.

Questo articolo esplora i giri e le loro implicazioni.

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