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Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

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This paper clarifies an integrable model for ultrashort pulse propagation, refuting a recent comment. The model

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Area of Science:

  • Nonlinear Optics
  • Mathematical Physics

Background:

  • A previously proposed integrable model for ultrashort pulse propagation has been questioned.
  • A recent comment suggested a flaw in the model's derivation.

Purpose of the Study:

  • To address and refute the claims made in a recent comment regarding the derivation of an integrable model.
  • To re-validate the proposed integrable model for ultrashort pulse propagation.

Main Methods:

  • Explicitly referencing the original paper to highlight the stated approximations.
  • Comparing the derived integrable model with the normalized Maxwell equation.
  • Comparing the model with other established integrable models.

Main Results:

  • The claim of a flaw in the derivation is demonstrated to be incorrect.
  • The necessity of a similar approximation in deriving the commented integrable equation is shown.
  • The integrable model is validated through comparisons with established physical models.

Conclusions:

  • The integrable model for ultrashort pulse propagation is robust and correctly derived.
  • The comment's assertion of a flaw is based on a misunderstanding of the stated approximations.
  • The model's validity is further supported by its consistency with the normalized Maxwell equation and other integrable models.