Transverse stability of plane solitons using the variational method
UNSPECIFIED. (1998) Transverse stability of plane solitons using the variational method. JOURNAL OF PLASMA PHYSICS, 59 (Part 3). pp. 543-554. ISSN 0022-3778Full text not available from this repository.
We present stability results for plane soliton solutions of two versions of the two-dimensional KdV equation, namely the Zakharov-Kuznetsov (ZK) equation and the Kadomtsev-Petviashvili equation for positive dispersion (KP+ equation). To do this we use a linear variation-of-action method (VAM). Others have used this method, but with little success when applied to these two equations. The best re suits have given the correct instability range, but the predicted growth rates have significant errors. For the ZK equation we show by paying more attention to the spatially asymptotic form of the trial function, how better estimates of the dispersion relation can be obtained. We go on to obtain the exact dispersion relation for Perturbations of the plane soliton solution of the KP+ equation.
|Item Type:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Journal or Publication Title:||JOURNAL OF PLASMA PHYSICS|
|Publisher:||CAMBRIDGE UNIV PRESS|
|Number of Pages:||12|
|Page Range:||pp. 543-554|
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