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• W2132197826 abstract "We consider the approximate control of solitons in generalized Korteweg--de Vries equations. By introducing a suitable internal bilinear control on the equation, we prove that any soliton is approximate null controllable, and, moreover, any soliton can be accelerated to any particular positive velocity, after a suitable large amount of time. Precise estimates on the error terms and the rate of decay in the approximate null controllability result are also given. Our method introduces a new insight into the control of nonlinear objects from the point of view of interaction and collision problems for nonlinear dispersive equations, recently developed by Martel and Merle [Ann. Math. (2), 174 (2011), pp. 757--857], [Invent. Math., 183 (2011), pp. 563--648]. It can be applied in principle to several other models with soliton solutions." @default.
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• W2132197826 date "2014-01-01" @default.
• W2132197826 modified "2023-10-02" @default.
• W2132197826 title "On Approximate Controllability of Generalized KdV Solitons" @default.
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• W2132197826 doi "https://doi.org/10.1137/120879701" @default.
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