On the orbital stability of Gaussian solitary waves in the log-KdV equation

@article{Carles2014OnTO,
  title={On the orbital stability of Gaussian solitary waves in the log-KdV equation},
  author={R{\'e}mi Carles and Dmitry E. Pelinovsky},
  journal={Nonlinearity},
  year={2014},
  volume={27},
  pages={3185 - 3202}
}
We consider the logarithmic Korteweg–de Vries (log-KdV) equation, which models solitary waves in anharmonic chains with Hertzian interaction forces. By using an approximating sequence of global solutions of the regularized generalized KdV equation in with conserved L2 norm and energy, we construct a weak global solution of the log-KdV equation in a subset of . This construction yields conditional orbital stability of Gaussian solitary waves of the log-KdV equation, provided that uniqueness and… 

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