# 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}
}
• Published 8 January 2014
• Mathematics
• Nonlinearity
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…
The logarithmic KdV (log-KdV) equation admits global solutions in an energy space and exhibits Gaussian solitary waves. Orbital stability of Gaussian solitary waves is known to be an open problem. We
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