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

  • Yong LiuEmail author
  • Juncheng Wei
Article
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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.

Notes

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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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