Orbital Stability of Waves in Hamiltonian Systems

  • Todd Kapitula
  • Keith Promislow
Part of the Applied Mathematical Sciences book series (AMS, volume 185)


Hamiltonian systems arise in a myriad of applications where damping can be neglected, from the motion of celestial bodies, to the spinning of rigid tops, to interactions of particles in molecular systems. They are also imbued with a rich structure that arises from the conservation of the underlying energy, the Hamiltonian, as well as other quantities such as mass and momentum. In this chapter we present a theory for the nonlinear stability of generalized traveling-wave solutions of Hamiltonian systems. This field has a long history, starting with a conjecture of Boussinesq, dating to 1872 [39], in which he suggested the constraint structure could be used to understand the stability of the critical points of the Hamiltonian.


Hamiltonian System Bilinear Form Homoclinic Orbit Essential Spectrum Nonlinear Stability 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Todd Kapitula
    • 1
  • Keith Promislow
    • 2
  1. 1.Department of Mathematics and StatisticsCalvin CollegeGrand RapidsUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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