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R. Killip, T. Tao and M. Visam, “The Cubic Nonlinear Schr?dinger Equation in Two Dimen-Sions with Radial Data,” Journal of the European Mathematical Society, Vol. 11, No. 6, 2009, pp. 1203-1258. doi:10.4171/JEMS/180

has been cited by the following article:

• 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.