Nonlinear Schrödinger — Bright Solitons
Self-focusing waves that never spread: perfect balance of dispersion and nonlinearity
NLS Parameters
Nonlinearity g:
2.0
Soliton velocity v:
1.0
Amplitude A:
1.0
Two-soliton mode:
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Norm ∫|ψ|² dx (conserved)
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Hamiltonian H (conserved)
iψ_t + ψ_xx + g|ψ|²ψ = 0
Bright soliton
solution: ψ(x,t) = A·sech(A√(g/2)·(x−vt))·e^{i(vx/2 − ωt)}
Exact balance: dispersion spreads the wave, nonlinearity focuses it. Enable two-soliton to see elastic collision — solitons pass through each other unchanged!
NLS appears in: optical fibers, Bose-Einstein condensates, water waves.