Derivation of Decoupled Korteweg–de Vries/Zakharov–Kuznetsov Equations from Vlasov–Poisson System in the Torus
Xiongfeng Yang, Lixian Zhao
Source abstract
Abstract. In this paper, we observe that the solutions of the Vlasov–Poisson (VP) system for ions in the torus [Formula: see text] converge to those of the decoupled Korteweg–de Vries/Zakharov–Kuznetsov equations in the long wavelength limit under the monokinetic distribution assumption. A rigorous justification is established from the delicate estimates of the relative entropy. Moreover, the two-way Kadomstev–Petviashvili equations are also established from the VP system when the magnetic field disappears. It extends the results about the limit from the VP system to the unidirectional packet as the solution of the limit equation in [D. Han-Kwan, Comm. Math. Phys., 324 (2013), pp. 961–993] to the two-directional waves as the solutions of decoupled limit equations in the fixed torus.
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