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Stabilized Kuramoto-Sivashinsky system.

B A Malomed1, B F Feng, T Kawahara

  • 1Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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This study introduces a new model for surface waves on liquid films, predicting stable solitary pulses and bound states. Numerical simulations confirm the model

Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Surface wave phenomena

Background:

  • Surface waves on multilayered liquid films exhibit complex behaviors.
  • Existing models may not fully capture the stability of solitary wave solutions.

Purpose of the Study:

  • To propose and analyze a novel model for surface waves on multilayered liquid films.
  • To investigate the existence and stability of solitary pulses and bound states within this model.

Main Methods:

  • Development of a mixed Kuramoto-Sivashinsky-Korteweg-de Vries equation coupled to a linear dissipative equation.
  • Application of perturbation theory, focusing on dissipation and gain as small perturbations.
  • Utilizing balance equations for net momentum.
  • Conducting direct numerical simulations to validate theoretical predictions.

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Main Results:

  • The proposed model allows for the stabilization of the zero solution, enabling stable solitary pulses.
  • Perturbation theory predicts the selection of two steady-state solitons from a continuous family.
  • Direct simulations confirm that the larger amplitude pulse is stable when the zero solution is stable.
  • Stable bound states of two and three pulses were numerically discovered.
  • An explanation for pulse stability even with an unstable zero background in limited domains was proposed.

Conclusions:

  • The developed model successfully predicts and describes stable solitary pulses and bound states in multilayered liquid films.
  • The interplay between dissipation, gain, and linear coupling is crucial for soliton selection and stability.
  • Numerical findings strongly support the theoretical predictions regarding pulse stability and the existence of bound states.