Asymptotic Stability of Lattice Solitons in the Energy Space

@article{Mizumachi2007AsymptoticSO,
  title={Asymptotic Stability of Lattice Solitons in the Energy Space},
  author={Tetsu Mizumachi},
  journal={Communications in Mathematical Physics},
  year={2007},
  volume={288},
  pages={125-144}
}
Orbital and asymptotic stability for 1-soliton solutions of the Toda lattice equations as well as for small solitary waves of the FPU lattice equations are established in the energy space. Unlike analogous Hamiltonian PDEs, the lattice equations do not conserve the adjoint momentum. In fact, the Toda lattice equation is a bidirectional model that does not fit in with the existing theory for the Hamiltonian systems by Grillakis, Shatah and Strauss. To prove stability of 1-soliton solutions, we… CONTINUE READING
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