Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations
J. A. Gonz\'alez, A. Bellor\'in, M. A. Garc\'ia-\~Nustes, L. E., Guerrero, S. Jim\'enez, L. V\'azquez
TL;DR
This paper proves that inhomogeneous long-range forces can induce an infinite number of internal shape modes in sine-Gordon solitons, expanding understanding of their complex internal dynamics.
Contribution
It demonstrates the existence of infinitely many internal modes in sine-Gordon solitons under specific inhomogeneous conditions, a novel theoretical insight.
Findings
Infinite internal modes exist in inhomogeneous sine-Gordon systems
Conditions for the existence of these modes are identified
The result broadens understanding of soliton internal dynamics
Abstract
We prove the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied.
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