These higher-dimensional effects enable emulation of:
Curved spacetime propagation,
Metric singularities from information collapse,
Horizons or event-like boundaries where waves can no longer escape (if dissipation is high enough).
This sets the stage for creating laboratory analogs of early universe conditions, where vacuum fluctuation and field excitation interplay to produce spatial structure and geometric response.
D. Analytical Behavior and Topological Excitations
Soliton-like States, Energy Bubbles, and Curvature Spikes
In the nonlinear information field dynamics governed by the equation:
2It2+Itc22I+I2I=B(x,t)\frac{\partial^2 I}{\partial t^2} + \gamma \frac{\partial I}{\partial t} - c^2 \nabla^2 I + \lambda |I|^2 I = B(\vec{x}, t)t22I+tIc22I+I2I=B(x,t)
specific regimes of the system support the formation of topologically stable, self-localized structures, akin to solitons, skyrmions, and energy bubbles. These structures are not merely mathematical curiosities but correspond to physically meaningful excitations that conserve localized energy and can sustain their identity over time and propagation distance, even under dissipative or noisy conditions.
1. Soliton-Like States
Solitons arise when nonlinear self-focusing (from the I2I\lambda |I|^2 II2I term) precisely balances the dispersive spreading (c22Ic^2 \nabla^2 Ic22I).
In 1D, the governing equation reduces under stationary ansatz I(x,t)=(x)eitI(x,t) = \phi(x) e^{-i\omega t}I(x,t)=(x)eit, yielding:
2(x)i(x)c2d2dx2+2=B(x)- \omega^2 \phi(x) - i \gamma \omega \phi(x) - c^2 \frac{d^2 \phi}{dx^2} + \lambda |\phi|^2 \phi = B(x)2(x)i(x)c2dx2d2+2=B(x)
In the absence of driving ( B(x)=0B(x) = 0B(x)=0 ) and small dissipation, this is formally analogous to the nonlinear Schrdinger equation (NLSE), which is known to support bright and dark solitons depending on the sign of \lambda. For >0\lambda > 0>0, bright solitons represent localized packets of concentrated information energy.
