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Convergence result for the short pulse equation

Author

Listed:
  • Giuseppe Maria Coclite

    (Politecnico di Bari, Dipartimento di Meccanica, Matematica e Management)

  • Lorenzo di Ruvo

    (Università di Bari, Dipartimento di Matematica)

Abstract

In this paper, we consider a non-local elliptic-hyperbolic system related to the short pulse equation. It is a model which describes the evolution of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides, including fused-silica telecommunication-type or photonic-crystal fibers, as well as hollow capillaries filled with transparent gases. We prove that the solution of a non-local elliptic-hyperbolic system related to the short pulse equation converges to the unique entropy one of the short pulse equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $$L^p$$ L p setting.

Suggested Citation

  • Giuseppe Maria Coclite & Lorenzo di Ruvo, 2026. "Convergence result for the short pulse equation," Partial Differential Equations and Applications, Springer, vol. 7(1), pages 1-30, March.
    • Handle: RePEc:spr:pardea:v:7:y:2026:i:1:d:10.1007_s42985-025-00364-9
    DOI: 10.1007/s42985-025-00364-9
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    References listed on IDEAS

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    1. Giuseppe Maria Coclite & Lorenzo di Ruvo, 2018. "Convergence of the regularized short pulse equation to the short pulse one," Mathematische Nachrichten, Wiley Blackwell, vol. 291(5-6), pages 774-792, April.
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