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Nondegeneracy, Morse Index and Orbital Stability of the KP-I Lump Solution

Abstract

Using Bäcklund transformation, we analyze the spectral property of the KP-I lump solution. It is proved that the lump is nondegenerate and its Morse index equals one. As a consequence, we show that it is orbitally stable.

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Acknowledgements

The research of Y. Liu is partially supported by “the Fundamental Research Funds for the Central Universities”. The research of J. Wei is partially supported by NSERC of Canada. Part of this work is finished while the first author is visiting the University of British Columbia in 2017. He thanks the institute for the financial support. We thank Prof. J. C. Saut for pointing out to us some key references. We also thank the anonymous referees for their valuable comments and suggestions.

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Correspondence to Yong Liu.

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Liu, Y., Wei, J. Nondegeneracy, Morse Index and Orbital Stability of the KP-I Lump Solution. Arch Rational Mech Anal 234, 1335–1389 (2019) doi:10.1007/s00205-019-01413-5

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