TITLE:
Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions
AUTHORS:
Pierre Hillion
KEYWORDS:
Soliton; Schrödinger Equation; Cubic Nonlinearity
JOURNAL NAME:
Optics and Photonics Journal,
Vol.2 No.3,
September
20,
2012
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.