By varying the nonlinear coefficient \lambda, we observe:
This demonstrates that nonlinearity controls the curvature depth and scale, supporting the idea that topology arises from field self-interaction strength, analogous to gravitational self-energy.
5. Implication for Cosmology: Proto-Metric Field Analogy
In gravitational theories, the metric tensor gg_{\mu\nu}g defines spacetime curvature. In our analog, the information field intensity I(x,t)I(x,t)I(x,t) and its nonlinear evolution acts as an emergent proto-metric, encoding:
Curvature magnitude via energy concentration
Geometric gradients via field flux variation
Topology via phase and amplitude soliton structures
Thus, the field does not simulate curvature by analogy alone---it generates curvature-like behavior intrinsically, grounded in physical interaction and resonance.
C. Topological Structures and Phase Defects
Formation of vortex-like defects, solitonic textures, and phase singularities as emergent topological markers
In this section, we explore how nonlinear blink excitation in the information field system not only produces localized energy and curvature analogs, but also leads to the emergence of topologically protected structures---such as phase defects, vortices, and solitonic textures---analogous to features observed in condensed matter, optics, and even early universe field theories.
1. Phase Defects and Vortices
By decomposing the complex field I(x,t)=A(x,t)ei(x,t)I(x,t) = A(x,t) e^{i \phi(x,t)}I(x,t)=A(x,t)ei(x,t), we analyze the spatial distribution of the phase field (x,t)\phi(x,t)(x,t).
Simulations show:
