 Fundamental temporal bright soliton

For positive Kerr nonlinearity and anomalous group velocity dispersion, the displayed sech envelope solves the ideal cubic fibre equation. Substitution uses $(\mathrm{sech}u{)}^{\prime \prime }=\mathrm{sech}u-2{\mathrm{sech}}^{3}u$. Dispersion and nonlinear lengths coincide. Higher-order corrections, attenuation and a delayed response can change actual propagation.