Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions

Pierre Hillion

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

DOI: 10.4236/opj.2012.23026                

Abstract

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.

Keywords

Soliton; Schrödinger Equation; Cubic Nonlinearity

Conflicts of Interest

The authors declare no conflicts of interest.

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