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Well-Posedness Results for the Continuum Spectrum Pulse Equation

Author

Listed:
  • Giuseppe Maria Coclite

    (Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125 Bari, Italy)

  • Lorenzo di Ruvo

    (Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125 Bari, Italy)

Abstract

The continuum spectrum pulse equation is a third order nonlocal nonlinear evolutive equation related to the dynamics of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides. In this paper, the well-posedness of the classical solutions to the Cauchy problem associated with this equation is proven.

Suggested Citation

  • Giuseppe Maria Coclite & Lorenzo di Ruvo, 2019. "Well-Posedness Results for the Continuum Spectrum Pulse Equation," Mathematics, MDPI, vol. 7(11), pages 1-39, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1006-:d:279260
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    References listed on IDEAS

    as
    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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    Cited by:

    1. Giuseppe Maria Coclite & Lorenzo Ruvo, 2022. "On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-40, December.

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    1. Giuseppe Maria Coclite & Lorenzo Ruvo, 2022. "On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-40, December.
    2. Giuseppe Maria Coclite & Lorenzo di Ruvo, 2020. "A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation," Mathematics, MDPI, vol. 8(10), pages 1-31, October.

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