Phase Solitons and Topological Stress Transport in a Coherence Field: From Transient Gradients to Persistent Structures

This preprint extends the coherence-field framework introduced in “Ampere Longitudinal Force as Transient Phase-Gradient Stress in a Coherence Field” (Zenodo, 2026, doi:10.5281/zenodo.18180865) by analyzing whether phase-gradient stress can self-organize into stable or long-lived structures.

We treat the undriven limit (∂tθ = 0) and classify solitonic and topological solutions (1D sine-Gordon kinks; 2D vortices with quantized winding) that transport stress and momentum internally while remaining compatible with standard conservation laws. We derive the phase-gradient stress tensor, provide explicit kink and vortex profiles, establish scaling relations for localization length and stress magnitude, and outline timing- and threshold-based experimental signatures that distinguish soliton-mediated stress transport from prompt electromagnetic impulses and late-time acoustic artifacts.

Related works (author):
- Paper I: “Ampere Longitudinal Force as Transient Phase-Gradient Stress in a Coherence Field” (doi:10.5281/zenodo.18180865)
- “A Coherence-Based Field Theory of Matter, Inertia, and Gravitation” (doi:10.5281/zenodo.18148829)