The Tanaka Instability of Traveling Waves in Hamiltonian Systems (Mathematical aspects of nonlinear waves and their applications)

IR (HANDLE) Open Access
  • Sato, Naoki
    Research Institute for Mathematical Sciences, Kyoto University
  • Yamada, Michio
    Research Institute for Mathematical Sciences, Kyoto University

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Description

This paper reviews the linear instability of nonlinear traveling waves in Hamiltonian systems subject to superharmonic perturbations. Tanaka's instability, characterized by a zero eigenvalue with geometric multiplicity of one and algebraic multiplicity equal to or greater than four, occurs in the presence of translationally symmetric traveling wave solutions at the extrema of energy with respect to wave speed. The theory finds application in the study of the superharmonic instability of wave equations with a Hamiltonian structure, such as water waves with constant vorticity.

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2153 58-66, 2020-04

    京都大学数理解析研究所

Details 詳細情報について

  • CRID
    1050567175332623744
  • NII Book ID
    AN00061013
  • ISSN
    18802818
  • HANDLE
    2433/255087
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB

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