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April 21, 2026Open Access

The sine-Gordon Equation — Foundations of Topological Soliton Theory

Key Points

The aim is to explore the mathematical foundations of the sine-Gordon equation and its implications for soliton theory.
Survey of mathematical structures pertaining to the sine-Gordon equation
Proof of preservation of soliton properties in a rectangular-wave limit
Development of a model for elastic collisions in a perfect fluid.
Demonstrated that all structural properties of solitons are maintained in the rectangular-wave limit.
Presented a viable model for perfectly elastic collisions at various phases in a specific fluid environment.

Abstract

This paper surveys the mathematical structure of the sine-Gordon equation, proves that all structural properties of solitons are preserved in the rectangular-wave limit, and presents an alternative model for perfectly elastic collisions at arbitrary phases in a perfect fluid with different specific gravities.

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The sine-Gordon Equation — Foundations of Topological Soliton Theory | Synapse

Cite This Study

Noriaki Kihara (Sun,) studied this question.

synapsesocial.com/papers/69e7143fcb99343efc98da5a https://doi.org/https://doi.org/10.5281/zenodo.19650966