Stretching Coordinates System/Reductive perturbation theory

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Ahmer ali

TL;DR: why stretching coordinate transformation is used in the study of solitons formation using reductive perturbation theory?
What is the physical reason behind the usually used transformation of the form mentioned below

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Dale

Mentor

Please link to the specific paper in question.

Ahmer ali

Dale said:

Please link to the specific paper in question.

Please find the link to the paper and the attached file contains that paper.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.17.996

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