Soliton interaction with external forcing within the Korteweg–de Vries equation

报告题目: Soliton interaction with external forcing within the Kortewegde Vries equation

报告人:Prof. Yury Stepanyants  (University of Southern Queensland, Australia)

时间:2018920日(星期四)15:30 -- 16:30



摘要:In many natural conditions, flows around obstacles generate solitary waves in the oceans (current over bottom hills), atmospheres (flows around mountains), plasmas (waves generated by moving charges or electric potentials), Bose–Einstein condensates (waves generated by moving probes), etc. Description of such processes can be adequately implemented within the framework of the forced Korteweg–de Vries equation, which contains an extra term characterising the shape and strength of external force. We consider the resonant interaction of a solitary wave (soliton) with the external pulse-type and periodic perturbations within such equation. In our analysis we use earlier developed by other authors an asymptotic method based on the weakness of external force, but relationship between the widths of a soliton and external perturbation can be arbitrary. It is shown that there are several regimes of solitary wave interaction with the external force, which can lead to soliton reflection from the forcing, transition through it, or capturing by it. In some case, solitons can emerge from small-amplitude random perturbations. In the meantime, in the number of particular cases the exact stationary solutions of the forced Korteweg–de Vries equation can be obtained even for the external force of arbitrary amplitude. Theoretical results obtained by asymptotic method are compared with the results of direct numerical modelling within the forced Korteweg–de Vries equation.


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