Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions - Optics and Photonics Journal

OPJ > Vol.2 No.3, September 2012

Optics and Photonics Journal

Volume 2, Issue 3 (September 2012)

ISSN Print: 2160-8881 ISSN Online: 2160-889X

Google-based Impact Factor: 0.85 Citations

Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions ()

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DOI: 10.4236/opj.2012.23026 7,735 Downloads 11,332 Views Citations

Author(s)

Pierre Hillion

Affiliation(s)

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

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

Share and Cite:

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.

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