Stability and instability of solitary waves of Korteweg-de Vries type

@article{Bona1987StabilityAI,
  title={Stability and instability of solitary waves of Korteweg-de Vries type},
  author={Jerry L. Bona and Panagiotis E. Souganidis and Walter A. Strauss},
  journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
  year={1987},
  volume={411},
  pages={395 - 412}
}
Considered herein are the stability and instability properties of solitary-wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear, dispersive long waves. Special cases for which our analysis is decisive include equations of the Korteweg-de Vries and Benjamin-Ono type. Necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be… Expand
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