Why are solitons stable

  title={Why are solitons stable},
  author={T. Tao},
  journal={Bulletin of the American Mathematical Society},
  • T. Tao
  • Published 2008
  • Physics, Mathematics
  • Bulletin of the American Mathematical Society
  • The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account, \emph{solitary wave} or \emph{soliton} solutions can be created, which can be stable enough to persist indefinitely. The construction of such solutions is relatively straightforward, but the fact that they are \emph{stable} requires some significant amounts of… CONTINUE READING
    96 Citations

    Paper Mentions

    Blog Post
    Bifurcation and Stability of Travelling Waves in Self-focusing Planar Waveguides
    • 20
    Nonlinearity Saturation as a Singular Perturbation of the Nonlinear Schrödinger Equation
    • 4
    • PDF
    Invariant measures and the soliton resolution conjecture
    • 15
    • PDF
    Aspects of the modified regularized long-wave equation
    • 1
    • PDF


    Linear Problems Related to Asymptotic Stability of Solitons of the Generalized KdV Equations
    • Y. Martel
    • Mathematics, Computer Science
    • SIAM J. Math. Anal.
    • 2006
    • 40
    On the focusing critical semi-linear wave equation
    • 88
    • PDF
    The Korteweg–deVries Equation: A Survey of Results
    • 497
    Existence of blow-up solutions in the energy space for the critical generalized KdV equation
    • 144
    • PDF
    Asymptotic stability of solitary wave solutions to the regularized long-wave equation
    • 25