Resonances in nonlinear Klein-Gordon kink scattering by impurities

  • Yuri S. Kivshar
  • Angel Sánchez
  • Luis Vázquez
Part VI: Mathematical Methods
Part of the Lecture Notes in Physics book series (LNP, volume 393)


The scattering of topological kinks by point-like impurities is numerically studied in the framework of the sine-Gordon and φ4 models. In the first case, we show that previous approximate analytical results are indeed applicable. Thus, for low velocities, the reflection coefficient depends oscillatorily on the distance between impurities, i.e., resonant scattering takes place. On the other hand, this effect disappears for higher velocities. This result is found to hold also for the φ4 model nonlinearly coupled to the impurities, whereas the linear coupling for the same model gives rise to a different behaviour.


Reflection Coefficient Resonant Scattering Linear Coupling Impurity Mode Envelope Soliton 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Yuri S. Kivshar
    • 1
    • 2
  • Angel Sánchez
    • 1
  • Luis Vázquez
    • 1
  1. 1.Departamento de Física Teórica IFacultad de Ciencias Físicas Universidad ComplutenseMadridSpain
  2. 2.Institute for Low Temperature Physics and EngineeringKharkovUSSR

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