Comment on "Orbital stability of solitary wave solutions for an interaction equation of short and long dispersive waves"

Details Comment on "Orbital stability of solitary wave solutions for an interaction equation of short and long dispersive waves" Comment on "Orbital stability of solitary wave solutions for an interaction equation of short and long dispersive waves"

2007-05-23

arxiv.org/abs/0705.3443v1

Mathematics

Analysis of PDEs

2 pages

Scientific paper

J. Angulo and J. F. Montenegro (J. Differential Equations 174 (2001), no. 1, 181-199) published a paper about nonlinear stability of solitary waves for an interaction system between a long internal wave and a short surface wave in a two layer fluid considering that the fluid depth of the lower layer is sufficiently large in comparison with the wavelength of the internal wave. In this note, we show that in a critical step during the proof of Lemma 2.4 in the above mentioned paper, there is a claim used by the authors which fails to be true. Lemma 2.4 is crucial for the proof of Lemma 2.7, and for the proof of stability in Theorem 2.1 in the paper before mentioned.

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