Author(s)

Pierre Hillion

Institut Henri Poincaré, 86 Bis Route de Croissy, Le Vésinet, France.

We first analyze the sech-shaped soliton solutions, either spatial or temporal of the 1D-Schr?dinger equation with a cubic nonlinearity. Afterwards, these solutions are generalized to the 2D-Schr?dinger equation in the same configuration and new soliton solutions are obtained. It is shown that working with dimensionless equations makes easy this generalization. The impact of solitons on modern technology is then stressed.

Soliton; Schrödinger Equation; Cubic Nonlinearity

Hillion, P. (2012) Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions. Optics and Photonics Journal, 2, 173-177. doi: 10.4236/opj.2012.23026.