Fundamental temporal bright soliton ($A=\sqrt{P_s}\mathrm{sech}(T/T_0)e^{i\gamma P_{s}z/2},\gamma P_s{T}_0^2=|{\beta }_2|$)

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.