On some classes of mKdV periodic solutions

@article{Kevrekidis2004OnSC,
  title={On some classes of mKdV periodic solutions},
  author={Panayotis G. Kevrekidis and Avinash Khare and Avadh B Saxena and G. Herring},
  journal={Journal of Physics A},
  year={2004},
  volume={37},
  pages={10959-10965}
}
We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV… 
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