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Related Experiment Videos

Moving lattice kinks and pulses: an inverse method.

S Flach1, Y Zolotaryuk, K Kladko

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

Researchers developed a general inverse method to map traveling-wave solutions to lattice equations of motion. This approach uniquely identifies potential functions for various nonlinear systems, including reaction-diffusion and discrete nonlinear Schrödinger models.

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Area of Science:

  • Nonlinear Dynamics
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • Traveling-wave solutions, such as kinks and pulses, are fundamental in describing complex phenomena in various physical systems.
  • Understanding the underlying equations of motion and potential functions that support these solutions is crucial for theoretical analysis and prediction.

Purpose of the Study:

  • To develop a general inverse method for mapping traveling-wave solutions to equations of motion on one-dimensional lattices.
  • To uniquely determine potential functions for systems supporting kink and pulse solutions.

Main Methods:

  • A general mapping (inverse method) is developed to relate traveling-wave solutions (kinks, pulses) and their velocities to lattice equations of motion.
  • The method is applied to diverse systems: acoustic solitons, nonlinear Klein-Gordon chains, reaction-diffusion equations, and discrete nonlinear Schrödinger systems.

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  • Conditions for the unique determination of potential functions are established, requiring reflection symmetry and sufficient smoothness (C2) of the wave shapes.

    • Main Results:

    • The inverse method successfully maps traveling-wave solutions to the equations of motion for the studied lattice systems.
    • Potential functions are uniquely determined for systems with reflection-symmetric pulse shapes and C2 kink/pulse shapes.
    • The method's connection to the Peierls-Nabarro potential and continuous symmetries is discussed for kink solutions.
    • Generalization to higher-dimensional lattices for reaction-diffusion systems is achieved, showing that increased component numbers facilitate moving solutions.

    Conclusions:

    • The developed inverse method provides a powerful tool for analyzing traveling-wave solutions in diverse nonlinear lattice systems.
    • This approach facilitates the unique identification of potential functions, advancing the understanding of soliton dynamics and related phenomena.
    • The generalization to higher dimensions and multi-component systems opens avenues for studying more complex dynamic behaviors.