Aktosun's Recent Preprints

T. Aktosun, F. Demontis, and C. van der Mee.
Exact solutions to the sineGordon equation.
arXiv/nlin.SI/1003.2453.
pdf version.

T. Aktosun and C. van der Mee.
Darboux transformation for the NLS equation.
pdf version.

T. Aktosun, T. Busse, F. Demontis, and C. van der Mee.
Symmetries for exact solutions to the nonlinear Schrödinger equation.
arXiv/nlin.SI/0905.4231.
Already appeared in: Journal of Physics A 43 (2010), no. 1, 025202.
pdf version.

T. Aktosun and C. van der Mee.
A unified approach to Darboux transformations.
arXiv/nlin.SI/0905.0520.
Already appeared in: Inverse Problems 25 (2009), no. 10, 105003.
pdf version.

T. Aktosun and Vassilis G. Papanicolaou.
Time evolution of the scattering data for a fourthorder linear differential operator.
arXiv/nlin.SI/0805.3554.
Already appeared in: Inverse Problems 24 (2008), no. 5, 055013.
pdf version.

T. Aktosun, T. Busse, F. Demontis, and C. van der Mee.
Exact solutions to the nonlinear Schrödinger equation.
arXiv/nlin.SI/0908.2684.
To appear in J. A. Ball, V. Bolotnikov, J. W. Helton,
L. Rodman, and I. M. Spitkovsky (eds.).
Topics in Operator Theory.
Birkhäuser series on Operator Theory: Advances and Applications, Vol. 203, pp. 112 (2010).
pdf version.

T. Aktosun.
Inverse Scattering Transform and the theory of solitons.
arXiv/nlin.SI/0905.4746.
Already appeared in: Encyclopedia of Complexity and Systems Science, by Springer.
pdf version.

T. Aktosun, F. Demontis, and C. van der Mee.
Exact solutions to the focusing nonlinear Schrödinger equation.
IMA Preprint #2157, February 2007.
arXiv/nlin.SI/0702010.
Already appeared in:Inverse Problems 23 (2007), no. 5, 21712195.
pdf version.
A
Mathematica notebook: n solitons (2.1 MB).
A Mathematica notebook: a
2soliton example (4.8 MB).
A Mathematica notebook: a
soliton with a double pole (5.2 MB). (Ignore Mathematica front end error message, it is a bug in Mathematica)

T. Aktosun.
Promoting undergraduate research.
Already appered in:
J. A. Gallian (ed.),
Proceedings of the conference on promoting undergraduate research in mathematics,
Am. Math. Soc.,
Providence, RI, 2007, pp. 167172.
pdf version.

T. Aktosun and C. van der Mee.
Explicit solutions to the Kortewegde Vries equation on the half line.
IMA Preprint #2122, May 2006.
Already appeared in: Inverse Problems
22 (2006), no. 6, 21652174.
pdf version (141 KB).
An example and its animation with no solitons as a Mathematica notebook (1.5 MB).
An example and its animation with
one soliton as a Mathematica notebook (1.6 MB).
An example and its animation with
two solitons as a Mathematica notebook (2.6 MB).

T. Aktosun and R. Weder.
The BorgMarchenko theorem with a continuous spectrum.
IMA Preprint #2070, October 2005
Already appeared in: N. Chernov, Y. Karpeshina, I. W. Knowles, R. T. Lewis, and R. Weikard, Recent advances in differential equations and mathematical physics,
Contemporary Mathematics, Vol. 412,
Am. Math. Soc., Providence, 2006, pp. 1530.
pdf version (220 KB).

T. Aktosun.
Inverse scattering to
determine the shape of a vocal tract.
Already appeared in:
M. A. Dritschel (ed.),
The extended field of operator theory,
Operator Theory: Advances and Applications, Vol. 171,
Birkhäuser, Basel, 2007, pp. 116.

T. Aktosun.
Inverse scattering for vowel articulation with frequencydomain data.
IMA Preprint #1996, October 2004
Already appeared in: Inverse Problems 21 (2005), no. 3, 899914.
pdf version (179 KB).

T. Aktosun,
M. H. Borkowski, A. J. Cramer, and L. C. Pittman.
Inverse scattering with rational scattering coefficients
and wave propagation in nonhomogeneous media
(based on the research performed during the 2003 REU program at Mississippi State University).
Already appeared in:
Rien Kaashoek, Sebastiano Seatzu, and Cornelis van der Mee (eds.)
The Proceedings of the Fourteenth International Conference on Operator Theory and Applications.
Birkhäuser series on Operator Theory, Vol 160, pp. 120 (2005).
pdf version (198 KB).

T. Aktosun,
and R. Weder.
Inverse spectralscattering problem
with two sets of discrete spectra
for the radial Schrödinger equation.
IMA Preprint #1960, February 2004
Already appeared in: Inverse Problems 22 (2006) , no. 1, 89114.
pdf version (310 KB).

T. Aktosun,
V. G. Papanicolaou, and V. Zisis.
Inverse scattering on the line for a
generalized nonlinear Schrödinger equation.
IMA Preprint #1955, January 2004
Already appeared in:
Inverse Problems 20 (2004), no. 4, 12671280.
pdf version (157 KB).

T. Aktosun.
Solitons and inverse scattering transform.
already appeared in: Dominic P. Clemence and Guoqing Tang (eds.)
Mathematical studies in nonlinear wave propagation,
Contemporary Mathematics, vol. 379,
Am. Math. Soc., Providence, 2005, pp. 4762.
pdf version (202 KB).

T. Aktosun.
Inverse scattering on the line
with incomplete scattering data.
IMA Preprint #1947, December 2003
already appeared in:
C. Conca, R. Manásevich, G. Uhlmann, and M. S. Vogelius (eds.)
Partial differential equations and inverse problems,
Contemporary Mathematics, vol. 362,
Am. Math. Soc., Providence, 2004, pp. 111.
pdf version (206 KB).

T. Aktosun and V. G. Papanicolaou.
Recovery of a potential from the ratio of reflection
and transmission coefficients.
IMA Preprint #1932, July 2003
Already appeared in: J. Math. Phys. 44 (2003), no. 11, 48754883.
pdf version (161 KB).

T. Aktosun.
Construction of the halfline potential from the Jost function.
IMA Preprint #1926, May 2003
Already appeared in:
Inverse Problems 20 (2004), no. 3, 859876.
pdf version (210 KB).

T. Aktosun.
Inverse scattering transform, KdV,
and solitons.
IMA Preprint #1927, May 2003
Already appeared in:
J. A. Ball, J. W. Helton, M. Klaus, and L. Rodman (eds.),
Current Trends in Operator Theory and Its Applications,
Birkhäuser, Basel, 2004, pp. 123.
pdf version (271 KB).

T. Aktosun and J. H. Rose.
Wave focusing on the line.
IMA Preprint #1800, July 2001
Already appeared in: J. Math. Phys. 43 (2002), no. 7, 37173745.
pdf version (345 KB).
Focusing Wave (QuickTime Movie, 24.5 MB)

T. Aktosun and R. Weder.
Inverse scattering with partial information on the potential.
IMA Preprint #1749, February 2001
Already appeared in: J. Math. Anal. Appl. 270 (2002),
no. 1, 247266.
pdf version (240 KB).
Tuncay Aktosun
aktosun@uta.edu
Last modified: March 11, 2010