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arXiv · 1706.00064

Normal form for transverse instability of the line soliton with a nearly critical speed of propagation

Dmitry E. Pelinovsky
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Abstract

There exists a critical speed of propagation of the line solitons in the Zakharov-Kuznetsov (ZK) equation such that small transversely periodic perturbations are unstable for line solitons with larger-than-critical speeds and orbitally stable for those with smaller-than-critical speeds. The normal form for transverse instability of the line soliton with a nearly critical speed of propagation is derived by means of symplectic projections and near-identity transformations. Justification of this normal form is provided with the energy method. The normal form predicts a transformation of the unstable line solitons with larger-than-critical speeds to the orbitally stable transversely modulated solitary waves.

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Dmitry E. Pelinovsky. 2017-10-03. Normal form for transverse instability of the line soliton with a nearly critical speed of propagation. https://arxiv.org/abs/1706.00064

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