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- W1517459239 abstract "Abstract. J. Angulo and J. F. Montenegro (J. Differential Equations 174(2001), no. 1, 181-199) published a paper about nonlinear stability of solitarywaves for an interaction system between a long internal wave and a short surfacewave in a two layer fluid considering that the fluid depth of the lower layer issufficiently large in comparison with the wavelength of the internal wave. Inthis note, we show that in a critical step during the proof of Lemma 2.4 in theabove mentioned paper, there is a claim used by the authors which fails to betrue. Lemma 2.4 is crucial for the proof of Lemma 2.7, and for the proof ofstability in Theorem 2.1 in the paper before mentioned.MSC: 35B35; 35Q51; 35Q35Keywords: Nonlinear stability; Solitary waves; Hilbert transform; Dispersivewaves Throughout this manuscript we keep the terminology and notations of [1] asmuch as possible. We start (see [1, Lemma 2.4, p. 188]) by remarking that applyingthe dominated convergence theorem, we getKh1c−K −1γ i(φ 0 f) 2 =1c 2 Z" @default.
- W1517459239 created "2016-06-24" @default.
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- W1517459239 date "2007-05-23" @default.
- W1517459239 modified "2023-09-27" @default.
- W1517459239 title "COMMENT ON ORBITAL STABILITY OF SOLITARY WAVE SOLUTIONS FOR AN INTERACTION EQUATION OF SHORT AND LONG DISPERSIVE WAVES" @default.
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