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