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

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.