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3. Benchmark Comparisons
To validate and benchmark the simulation model, we compared our results with known analytical and numerical models from three categories:
a. Linear Wave Propagation
For =0\lambda = 0=0, the model reduces to a damped wave equation.
Numerical propagation speed and damping decay matched analytical solutions:
I(x,t)et/2sin(kxt)I(x,t) \sim e^{-\gamma t/2} \sin(kx - \omega t)I(x,t)et/2sin(kxt)
Relative error in amplitude and phase: < 1.5%.
b. Nonlinear Schrdinger Limit (NLS)
For slow envelope approximation and weak damping:
I(x,t)A(x,t)ei(kxt),A governed by NLSI(x,t) \sim A(x,t) e^{i(kx - \omega t)}, \quad A \text{ governed by NLS}I(x,t)A(x,t)ei(kxt),A governed by NLS
Compared to NLS soliton profiles:
Shape fidelity: > 98% overlap.
Soliton width and velocity matched within 2% error.
c. Bifurcation Thresholds
Simulated bifurcation diagrams (see Appendix II) were compared with literature models (e.g., Ginzburg--Landau systems, sine-Gordon breathers).
4. Code Availability and Structure
We provide a minimal working example (MWE) script including:
field_solver.py -- contains core PDE integrator
initial_conditions.py -- pulse designer
visualize.py -- spatiotemporal plotters and Fourier diagnostics
run_simulation.py -- main loop driver
params.yaml -- config file for parameter sweeping
Benchmark dataset (HDF5, ~1.2 GB) is available for:
