On instability of solitons in the 2d cubic Zakharov–Kuznetsov equation
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We study the flow map associated to the cubic Schrödinger equation in space dimension at least three. We consider initial data of arbitrary size in Hs, where 0 < s < sc, sc the critical index, and perturbations in Hσ , where σ < sc is independent of s. We show an instability mechanism in some Sobolev spaces of order smaller than s. The analysis relies on two features of super-critical geometric...
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ژورنال
عنوان ژورنال: São Paulo Journal of Mathematical Sciences
سال: 2019
ISSN: 1982-6907,2316-9028
DOI: 10.1007/s40863-019-00142-7