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arXiv · 2504.17580

Linear Test Approach to Global Controllability of Higher-Order Nonlinear Dispersive Equations with Finite-Dimensional Control

Debanjit Mondal
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Abstract

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.

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Debanjit Mondal. 2025-04-24. Linear Test Approach to Global Controllability of Higher-Order Nonlinear Dispersive Equations with Finite-Dimensional Control. https://arxiv.org/abs/2504.17580

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