Split-step Fourier method — solitons, dispersion, and two-soliton collision
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Norm: —Peak |ψ|²: —Mode: Single
The Nonlinear Schrödinger equation iψ_t = −½ψ_xx − g|ψ|²ψ describes light in optical fibers, Bose-Einstein condensates, and water waves. Dispersion wants to spread wave packets; nonlinearity (self-focusing) counteracts it. At the right balance, solitons — stable, shape-preserving pulses — emerge. Two solitons collide and pass through each other unchanged — a hallmark of integrability. Computed via split-step Fourier method: evolve kinetic term in frequency space, potential in position space.