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Canonical coordinates for plasma and hydrodynamic problems.

K M Case1, A M Roos

  • 1The Rockefeller University, New York, New York 10021.

Proceedings of the National Academy of Sciences of the United States of America
|December 1, 1981
PubMed
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Researchers identified canonical coordinates and momenta for nonlinear equations in plasma physics, hydrodynamics, and solid-state physics. This facilitates the application of Hamiltonian mechanics to these complex systems.

Area of Science:

  • Physics
  • Applied Mathematics

Background:

  • Many nonlinear equations in plasma physics, hydrodynamics, and solid-state physics possess Hamiltonian structures.
  • Utilizing the Hamiltonian form requires knowledge of canonical coordinates and momenta.

Purpose of the Study:

  • To exhibit canonical coordinates and momenta for key classes of nonlinear equations.
  • To enable the full application of Hamiltonian mechanics to these systems.

Main Methods:

  • Identification of canonical coordinates and momenta.
  • Analysis of nonlinear equations within Hamiltonian frameworks.

Main Results:

  • Canonical coordinates and momenta were successfully exhibited for three major classes of equations.
  • These classes encompass nearly all known completely integrable Hamiltonian systems.

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Conclusions:

  • The identification of canonical coordinates simplifies the analysis of complex nonlinear systems.
  • This work provides a foundational tool for studying integrable Hamiltonian systems across multiple physics disciplines.