On the stability of internal waves

@article{Kalisch2010OnTS,
  title={On the stability of internal waves},
  author={Henrik Kalisch and Nguyet Thanh Nguyen},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2010},
  volume={43},
  pages={495205}
}
The extended KdV equation ut + uux + αu2ux + uxxx = 0 is widely used as a model describing internal waves in ideal fluids. The equation admits a family of negative and positive solitary waves Φc. These solitary waves exhibit the typical broadening effect seen in internal waves. It is shown here that all solitary-wave solutions of the extended KdV equation are orbitally stable. The proof of stability is based on the general theory of Grillakis et al (1987 J. Funct. Anal. 74 160) for equations of… 

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