AKSSpectral

AKSSpectral is an application designed for spectral problems that does not require a desktop CAS. The workflow is intentionally split into multiple tabs, reflecting the way I actually use these tools: setting a potential energy, running forward spectral problems, checking scattering data, inverting, and then cross checking based on analytical solitons and conservation laws. The "Workspace" tab saves the shared state - your current u (x), v (x), domain, and any forward data you have calculated - so you won't re-enter the same seconds on every screen. Spectrum integrates the AKNS system with RK2 or RK4, allowing you to select preset or type expressions (sech, exp, trig) and plot optional superposition of Jost function amplitude and input potential. Scattering scan λ is used to estimate | a (λ) | and | b (λ)], label the binding state poles, and support phase/log views for fast robustness checks. IST uses an optional Marchenko style kernel to reconstruct u (x) from cached S-matrix data through Tikhonov regularization and optional side-by-side comparison with the original configuration file. Solitan constructs light, dark, and breathing curves with adjustable N, speed, and time - which is convenient when you need a reference waveform next to the digital output. The law recursively generates the first few conserved densities and shows that the dual Hamiltonian pair (H ₁, H ₂) AKNS hierarchy should satisfy.