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Identifying coherent structures in nonlinear wave propagation.

William I. Newman1, David K. Campbell, James M. Hyman

  • 1Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.

Chaos (Woodbury, N.Y.)
|July 1, 1991
PubMed
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A new method identifies solitary wave speeds and numbers in nonlinear wave phenomena. This approach works even when waves interact, aiding analysis in complex systems like plasma turbulence.

Area of Science:

  • Physics
  • Applied Mathematics

Background:

  • Nonlinear wave phenomena commonly exhibit solitary waves, which are coherent structures whose speed depends on amplitude and morphology.
  • Analyzing these solitary waves is crucial for understanding complex systems, but their interactions often complicate analysis.

Purpose of the Study:

  • To develop and present a novel method for identifying the number and speeds of independent solitary wave features.
  • To assess the method's effectiveness across various models, from simple analytical cases to complex numerical simulations.

Main Methods:

  • The proposed method assumes non-interacting time intervals for solitary wave structures.
  • It is applied to a Gaussian model, multisoliton solutions of the Korteweg-de Vries equation, and plasma turbulence simulations.

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Main Results:

  • The method successfully identified independent features and their speeds in diverse scenarios.
  • Performance varied, highlighting both the strengths and limitations of the current approach.

Conclusions:

  • The developed method offers a valuable tool for analyzing solitary wave dynamics in nonlinear systems.
  • Further research is suggested to refine the method and expand its applicability to more complex wave interactions.