Bright soliton in anomalous-dispersion fibre: A(z,t) = √P_0 sech(t/T_0) exp(iγP_0 z/2)

Hasegawa-Tappert 1973 bright soliton. In a fibre with anomalous group-velocity dispersion β_2 < 0 and Kerr non-linearity γ > 0, the slowly-varying envelope A(z,t) satisfies the non-linear Schrödinger equation i·∂A/∂z − (β_2/2)·∂²A/∂t² +…