Nonlinear Schroedinger Equation Note: Some of this information is in latex accompanied by its postscript form. If you do not have a postscript viewer for Windows, you can download it from the following web site: downloading ghostscript/ghostview. Below I have made this information available in pdf as well.

Descriptions of the NLSE from Sulem Catherine and Sulem Pierre-Louis, "The Nonlinear Schroedinger Equation: Self-Focusing and Wave Collapse", Applied Mathematical Sciences 139, Springer-Verlag, 1999. (as latex file)(as postscript file) (as pdf file)

Abstract: Nuclear Matter as a Nonlinear Optical Medium and the Nonlinear Schroedinger Equation (as latex file)(as postscript file) (as pdf file)

Solution of a Nonlinear Schroedinger Equation with a Bistable Potential (as latex file)(as postscript file) (as pdf file)

Diagrams and Calculations

Note that this work is based on Dr. M. Razavy's paper on An exactly soluble Schroedinger equation with a bistable potential, in Am. J. Phys., Vol. 48, No. 4, Apr. 1980, pp. 285-288.

Excerpts from Theory of Bose-Einstein condensation in trapped gases, Reviews of Modern Physics, Volume 71, No. 3, April 1999, pp. 463-512 (as latex file)(as postscript file) (as pdf file)

Overheads for the nuclear matter as a nonlinear optical medium part of the talk (from Dr. G. Papini's paper on "Nuclear Matter as a Nonlinear Optical Medium", Lettere al Nuovo Cimento, Vol. 17, No. 12, Nov. 1976, pp. 419-420)

List of References

Note: Dr. Valluri and I will also provide a proof of how the sech solution of the nonlinear Schroedinger Equation leads to higher harmonic solutions as described in the Gross-Pitaevskii Equation for Bose Einstein Condensation. This work will be in a separate paper. I will also add a section of pertinent excerpts from N. Akozbek and S. John's paper on Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures, Physical Review E, Vol. 57, No. 2, Feb. 1998, pp. 2287-2319.