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Kink-soliton explosions in generalized Klein–Gordon equations

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  • González, J.A.
  • Bellorín, A.
  • Guerrero, L.E.

Abstract

We investigate the dynamics of kink-solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We present different mechanisms for kink-soliton explosion and show that, in some cases while some analytically obtained conditions are satisfied, the kink-soliton breaks up becoming a permanent, extremely complex, spatiotemporal dynamics. We perform computer simulations in order to visualize and corroborate our analytical findings. The mechanisms presented for kink-soliton breakup can explain some of the phenomena that recently have been reported to occur in excitable media. Finally, we will present a way to control soliton breakup, using appropriate external perturbations.

Suggested Citation

  • González, J.A. & Bellorín, A. & Guerrero, L.E., 2007. "Kink-soliton explosions in generalized Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 143-155.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:143-155
    DOI: 10.1016/j.chaos.2006.10.047
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