Aktosun's Publications


  1. T. Aktosun and V. G. Papanicolaou
    Inverse problem with transmission eigenvalues for the discrete Schrödinger equation.
    Journal of Mathematical Physics 56 (2015), 082101.

  2. T. Aktosun, P. Sacks, and M. Unlu.
    Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials.
    Journal of Mathematical Physics 56 (2015), 022106.

  3. T. Aktosun and V. G. Papanicolaou
    Transmission eigenvalues for the self-adjoint Schrödinger operator on the half line.
    Inverse Problems 30 (2014), 075001.

  4. T. Aktosun, M. Klaus, and R. Weder.
    Small-energy analysis for the self-adjoint matrix Schrödinger operator on the half line. II.
    Journal of Mathematical Physics 55 (2014), 032103.

  5. T. Aktosun and V. G. Papanicolaou
    Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation.
    Inverse Problems 29 (2013), 065007.

  6. T. Aktosun and R. Weder.
    High-energy analysis and Levinson's theorem for the self-adjoint matrix Schrödinger operator on the half line.
    Journal of Mathematical Physics 54 (2013), 012108.

  7. T. Aktosun, D. Gintides, and V. G. Papanicolaou
    The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation.
    Inverse Problems 27 (2011), 115004.

    Unique recovery of Inhomogeneity from transmission eigenvalues
    Research Insights on Inverse Problems (related to the above article)

  8. T. Aktosun, M. Klaus, and R. Weder.
    Small-energy analysis for the self-adjoint matrix Schrödinger operator on the half line.
    Journal of Mathematical Physics 52 (2011), 102101.

  9. T. Aktosun, F. Demontis, and C. van der Mee.
    Exact solutions to the sine-Gordon equation.
    Journal of Mathematical Physics 51 (2010), 123521.
    [MR2779623].

  10. T. Aktosun and C. van der Mee.
    Darboux transformation for the NLS equation.
    In: Wen-Xiu Ma, Xing-biao Hu, and Qingping Liu (eds.).
    Nonlinear and modern mathematical physics
    .
    American Institute of Physics, Melville, NY, pp. 254-263 (2010).
    [MR2648968] [Zbl pre05882160].

  11. T. Aktosun, T. Busse, F. Demontis, and C. van der Mee.
    Symmetries for exact solutions to the nonlinear Schrödinger equation.
    Journal of Physics A 43 (2010), 025202.
    [Zbl 1189.37074].

  12. T. Aktosun, T. Busse, F. Demontis, and C. van der Mee.
    Exact solutions to the nonlinear Schrödinger equation.
    In: J. A. Ball, V. Bolotnikov, J. W. Helton, L. Rodman, and I. M. Spitkovsky (eds.).
    Topics in Operator Theory, Vol. 2: Systems and mathematical physics
    .
    Operator Theory: Advances and Applications, Vol. 203, Birkhäuser, Basel, pp. 1-12 (2010).
    arXiv/nlin.SI/0908.2684.
    [MR2683234] [Zbl 1190.37078].

  13. T. Aktosun and C. van der Mee.
    A unified approach to Darboux transformations.
    Inverse Problems 25 (2009), no. 10, 105003.
    [MR2545972 (2010k:45021)] [Zbl 1185.45006].

  14. T. Aktosun.
    Inverse Scattering Transform and the theory of solitons.
    In: R. A. Meyers (ed.).
    Encyclopedia of Complexity and Systems Science
    .
    Springer, New York, 2009, pp. 4960-4971.
    arXiv/nlin.SI/0905.4746.

  15. T. Aktosun and V. G. Papanicolaou.
    Time evolution of the scattering data for a fourth-order linear differential operator.
    Inverse Problems 24 (2008), no. 5, 055013.
    [MR2277535] [Zbl pre05363106].

  16. T. Aktosun, F. Demontis, and C. van der Mee.
    Exact solutions to the focusing nonlinear Schrödinger equation.
    Inverse Problems 23 (2007), no. 5, 2171-2195.
    [MR2353334] [Zbl 1126.35058].

  17. T. Aktosun.
    Promoting undergraduate research.
    In: J. A. Gallian (ed.),
    Proceedings of the conference on promoting undergraduate research in mathematics.

    Am. Math. Soc., Providence, RI, 2007, pp. 167-172.

  18. T. Aktosun.
    Inverse scattering to determine the shape of a vocal tract.
    In: M. A. Dritschel (ed.),
    The extended field of operator theory,

    Operator Theory: Advances and Applications, Vol. 171,
    Birkhäuser, Basel, 2007, pp. 1-16.
    [MR2308554] [Zbl 1110.35097].

  19. T. Aktosun and C. van der Mee.
    Explicit solutions to the Korteweg-de Vries equation on the half line.
    Inverse Problems 22 (2006), no. 6, 2165-2174.
    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).
    [MR2277535] [Zbl 1105.35099].

  20. T. Aktosun and R. Weder.
    The Borg-Marchenko theorem with a continuous spectrum.
    In: N. Chernov, Y. Karpeshina, I. W. Knowles, R. T. Lewis, and R. Weikard (eds.),
    Recent advances in differential equations and mathematical physics,

    Contemporary Mathematics, Vol. 412,
    Am. Math. Soc., Providence, 2006, pp. 15-30.
    [MR2259097] [Zbl 1108.34009].

  21. T. Aktosun and R. Weder.
    Inverse spectral-scattering problem with two sets of discrete spectra for the radial Schrödinger equation.
    Inverse Problems 22 (2006), no. 1, 89-114.
    [MR2194186 (2006j:34022)] [Zbl 1096.34064].

  22. B. J. Forbes, E. R. Pike, D. B. Sharp, and T. Aktosun.
    Inverse potential scattering in duct acoustics.
    Journal of the Acoustical Society of America 119 (2006), no. 1, 65-73.

  23. T. Aktosun, M. H. Borkowski, A. J. Cramer, and L. C. Pittman.
    Inverse scattering with rational scattering coefficients and wave propagation in nonhomogeneous media.
    In: R. Kaashoek, S. Seatzu, and C. van der Mee (eds.),
    Recent advances in operator theory and its applications,

    Operator Theory: Advances and Applications, Vol. 160,
    Birkhäuser, Basel, 2005, pp. 1-20.
    [MR2191081] [Zbl 1096.34006].

  24. T. Aktosun.
    Solitons and inverse scattering transform.
    In: Dominic P. Clemence and Guoqing Tang (eds.),
    Mathematical studies in nonlinear wave propagation,

    Contemporary Mathematics, Vol. 379,
    Am. Math. Soc., Providence, 2005, pp. 47-62.
    [MR2149045 (2006e:35335)] [Zbl 1086.35085].

  25. T. Aktosun.
    Inverse scattering for vowel articulation with frequency-domain data.
    Inverse Problems 21 (2005), no. 3, 899-914.
    [MR2144810 (2006a:35305)] [Zbl 1084.35117].

  26. T. Aktosun.
    Inverse scattering on the line with incomplete scattering data.
    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. 1-11.
    [MR2091487 (2005g:34025)] [Zbl 1072.34010].

  27. T. Aktosun.
    Inverse scattering transform, KdV, and solitons.
    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. 1-22.
    [MR2063745 (2005b:37165)] [Zbl 1062.37087].

  28. T. Aktosun, V. G. Papanicolaou, and V. Zisis.
    Inverse scattering on the line for a generalized nonlinear Schrödinger equation.
    Inverse Problems 20 (2004), no. 4, 1267-1280.
    [MR2087990 (2005d:34022)] [Zbl 1063.34006].

  29. T. Aktosun.
    Construction of the half-line potential from the Jost function.
    Inverse Problems 20 (2004), no. 3, 859-876.
    [MR2067505 (2005k:34331)] [Zbl 1071.34006].
    Corrigendum.
    Inverse Problems 20 (2004), no. 4, 1355.
    [MR2087996] [Zbl pre02124990].

  30. T. Aktosun and V. G. Papanicolaou.
    Recovery of a potential from the ratio of reflection and transmission coefficients.
    J. Math. Phys. 44 (2003), no. 11, 4875-4883.
    [MR2014834 (2004h:81265)] [Zbl 1062.81147].

  31. T. Aktosun and R. Weder.
    Inverse scattering with partial information on the potential.
    J. Math. Anal. Appl. 270 (2002), no. 1, 247-266.
    [MR1911764 (2003f:34169)] [Zbl 1012.34080].

  32. T. Aktosun and J. H. Rose.
    Wave focusing on the line.
    J. Math. Phys. 43 (2002), no. 7, 3717-3745.
    Focusing wave (QuickTime Movie, 24.5 MB)
    [MR1908696 (2003h:35148)] [Zbl 1060.35066].

  33. T. Aktosun and P. E. Sacks.
    Potential splitting and numerical solution of the inverse scattering problem on the line.
    Math. Methods Appl. Sci. 25 (2002), no. 4, 347-355.
    Quicktime animation of the solution of the KdV equation (1.9 MB).
    [MR1875708 (2002j:34145)] [Zbl 1054.34137].

  34. T. Aktosun, M. Klaus, and C. van der Mee.
    Small-energy asymptotics of the scattering matrix for the matrix Schrödinger equation on the line.
    J. Math. Phys. 42 (2001), no. 10, 4627-4652.
    [MR1855088 (2002j:81269)] [Zbl 1017.81046].

  35. T. Aktosun and M. Klaus.
    Chapter 2.2.4: Inverse theory: problem on the line.
    In: E. R. Pike and P. C. Sabatier (eds.),
    Scattering,

    Academic Press, London, 2001, pp. 770-785.

  36. T. Aktosun and M. Klaus.
    Small-energy asymptotics for the Schrödinger equation on the line.
    Inverse Problems 17 (2001), no. 4, 619-632.
    [MR1861473 (2002h:34182)] [Zbl 0989.81129].

  37. T. Aktosun, M. Klaus, and C. van der Mee.
    Direct and inverse scattering for selfadjoint Hamiltonian systems on the line.
    Integral Equations Operator Theory 38 (2000), no. 2, 129-171.
    [MR1791049 (2002e:34141)] [Zbl 0970.34072].

  38. T. Aktosun.
    Factorization and small-energy asymptotics for the radial Schrödinger equation.
    J. Math. Phys. 41 (2000), no. 7, 4262-4270.
    [MR1765585 (2001g:81265)] [Zbl 0973.81129].

  39. T. Aktosun and P. E. Sacks.
    Phase recovery with nondecaying potentials.
    Inverse Problems 16 (2000), no. 3, 821-838.
    [
    MR 2002d:34018a] [Zbl 0962.35183].
    Erratum.
    Inverse Problems 17 (2001), no. 2, 364.
    [MR1838234 (2002d:34018b)] [Zbl 0980.35171].

  40. T. Aktosun.
    Darboux transformation for the Schrödinger equation with steplike potentials.
    J. Math. Phys. 41 (2000), no. 4, 1619-1631.
    [MR1751849 (2001h:81266)] [Zbl 0977.81012].

  41. T. Aktosun, M. Klaus, and C. van der Mee.
    Integral equations in inverse scattering,
    In: J. K. Lu and G. C. Wen (eds.),
    Boundary value problems, integral equations and related problems,
    World Scientific Publ., River Edge, NJ, 2000, pp. 13-22.
    [MR1824377 (2002a:81331)] [Zbl 0980.45004].

  42. T. Aktosun and P. E. Sacks.
    Inversion of reflectivity data for nondecaying potentials.
    SIAM J. Appl. Math. 60 (2000), no. 4, 1340-1356.
    [MR1760038 (2001b:81156)] [Zbl 0956.34073].

  43. T. Aktosun.
    On the Schrödinger equation with steplike potentials.
    J. Math. Phys. 40 (1999), no. 11, 5289-5305.
    [MR1722311 (2000j:81274)] [Zbl 0968.81020].

  44. T. Aktosun and M. Klaus.
    Asymptotics of the scattering coefficients for a generalized Schrödinger equation.
    J. Math. Phys. 40 (1999), no. 8, 3701-3709.
    [MR1702436 (2000d:34180)] [Zbl 0953.34071].

  45. T. Aktosun, M. Klaus, and C. van der Mee.
    On the number of bound states for the one-dimensional Schrödinger equation.
    J. Math. Phys. 39 (1998), no. 9, 4249-4256.
    [MR1643229 (99j:81026)] [Zbl 0931.34069].

  46. T. Aktosun, M. Klaus, and C. van der Mee.
    Wave scattering in 1-D nonconservative media.
    In: A. G. Ramm (ed.),
    Spectral and scattering theory,

    Plenum Press, New York, 1998, pp. 1-18.
    [MR1625267 (99d:34163)] [Zbl 0903.34073].

  47. T. Aktosun, M. Klaus, and C. van der Mee.
    Inverse scattering in one-dimensional nonconservative media.
    Integral Equations Operator Theory 30 (1998), no. 3, 279-316.
    [MR1608677 (99b:34136)] [Zbl 0916.34070].

  48. T. Aktosun, M. Klaus, and C. van der Mee.
    Wave scattering in one dimension with absorption.
    J. Math. Phys. 39 (1998), no. 4, 1957-1992.
    [MR1614734 (99b:34137)] [Zbl 1001.34074].

  49. T. Aktosun and P. Sacks.
    Inverse problem on the line without phase information.
    Inverse Problems 14 (1998), no. 2, 211-224.
    [
    MR1619433 (98m:34026)] [Zbl 0902.34011].

  50. T. Aktosun, M. Klaus, and C. van der Mee.
    The one-dimensional inverse scattering problem for nonhomogeneous media with discontinuous wavespeed.
    In: D. Hinton and P. W. Schaefer (eds.),
    Spectral theory and computational methods of Sturm-Liouville problems,

    Lecture Notes in Mathematics, Vol. 191,
    Marcel Dekker, New York, 1997, pp. 105-133.
    [MR1460548 (98h:34142)] [Zbl 0883.34077].

  51. T. Aktosun, M. Klaus, and C. van der Mee.
    Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equations.
    J. Math. Phys. 37 (1996), no. 12, 5897-5915.
    [MR1419143 (97j:34111)] [Zbl 0910.34069].

  52. T. Aktosun, M. Klaus, and C. van der Mee.
    Integral equation methods for the inverse problem with discontinuous wave speed.
    J. Math. Phys. 37 (1996), no. 7, 3218-3245.
    [MR1401224 (97f:81169)] [Zbl 0897.34018].

  53. T. Aktosun, M. Klaus, and C. van der Mee.
    Recovery of discontinuities in a non-homogeneous medium.
    Inverse Problems 12 (1996), no. 1, 1-25.
    [MR1377128 (96m:34019)] [Zbl 0848.34070].

  54. T. Aktosun.
    Inverse Schrödinger scattering on the line with partial knowledge of the potential.
    SIAM J. Appl. Math. 56 (1996), no.1, 219-231.
    [MR1372897 (96m:81250)] [Zbl 0844.34016].

  55. T. Aktosun, M. Klaus, and C. van der Mee.
    On the recovery of a discontinuous wavespeed in wave scattering in a nonhomogeneous medium.
    In: D. Ivanchev and D. Mishev (eds.),
    Applications of mathematics in Engineering,
    Institute of Applied Mathematics and Informatics, Technical University, Sofia, 1995, pp. 9-27.

  56. T. Aktosun, M. Klaus, and C. van der Mee.
    Inverse scattering problem for the wave equation with discontinuous wavespeed.
    In: D. Bainov and V. Covachev (eds.),
    Proceedings of the Fifth International Colloquium on Differential Equations: Plovdiv, Bulgaria, 18-23 August, 1994,

    VSP, Utrecht, 1995, pp. 3-21.
    [MR1458342 (98d:34115)] [Zbl 0843.34079].

  57. T. Aktosun, M. Klaus, and C. van der Mee.
    Inverse wave scattering with discontinuous wave speed.
    J. Math. Phys. 36 (1995), no. 6, 2880-2928.
    [MR1331294 (96k:34181)] [Zbl 0843.34080].

  58. T. Aktosun.
    Bound states and inverse scattering for the Schrödinger equation in one dimension.
    J. Math. Phys. 35 (1994), no. 12, 6231-6236.
    [MR1303042 (95i:81262)] [Zbl 0822.34070].

  59. T. Aktosun and C. van der Mee.
    Inverse scattering in one dimension for a generalized Schrödinger equation.
    In: H. V. von Geramb (ed.),
    Quantum inversion theory and applications,

    Lecture Notes in Phys., Vol. 427,
    Springer, Berlin, 1994, pp. 37-49.
    [MR1267769 (95b:81221)] [Zbl 0797.34084].

  60. T. Aktosun and C. van der Mee.
    Nonuniqueness in inverse acoustic scattering on the line.
    J. Math. Phys. 35 (1994), no. 2, 693-709.
    [MR1257541 (94m:34031)] [Zbl 0806.34014].

  61. T. Aktosun.
    Scattering and inverse scattering for a second-order differential equation.
    J. Math. Phys. 34 (1993), no. 5, 1619-1634.
    [MR1214478 (94f:34164)] [Zbl 0773.34011].

  62. T. Aktosun, M. Klaus, and C. van der Mee.
    On the Riemann-Hilbert problem for the one-dimensional Schrödinger equation.
    J. Math. Phys. 34 (1993), no. 7, 2651-2690.
    [MR1224170 (95f:34130)] [Zbl 0777.34056].

  63. T. Aktosun.
    A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension.
    J. Math. Phys. 33 (1992), no. 11, 3865-3869.
    [MR1185863 (94b:81136)] [Zbl 0762.35075].

  64. T. Aktosun, M. Klaus, and C. van der Mee.
    Explicit Wiener-Hopf factorization for certain nonrational matrix functions.
    Integral Equations Operator Theory 15 (1992), no. 6, 879-900.
    [MR1188785 (93j:47030)] [Zbl 0790.47012].

  65. T. Aktosun, M. Klaus, and C. van der Mee.
    Scattering and inverse scattering in one dimensional nonhomogeneous media.
    J. Math. Phys. 33 (1992), no. 5, 1717-1744.
    [MR1158993 (93g:81200)] [Zbl 0760.35032].

  66. T. Aktosun, M. Klaus, and C. van der Mee.
    Inverse scattering in 1-D nonhomogeneous media and the recovery of the wave speed.
    J. Math. Phys. 33 (1992), no. 4, 1395-1402.
    [MR1154018 (92m:81300)] [Zbl 0756.34083].

  67. T. Aktosun and C. van der Mee.
    Wiener-Hopf factorization in multidimensional inverse Schrödinger scattering.
    In: D. H. Sattinger, C. A. Tracy, and S. Venakides (eds.),
    Inverse scattering and applications,

    Contemporary Mathematics, Vol. 122,
    Amer. Math. Soc., Providence, 1991, pp. 1-11.
    [MR1135851 (92g:35163)] [Zbl 0742.35044].

  68. T. Aktosun and C. van der Mee.
    Scattering and inverse scattering for the 1-D Schrödinger equation with energy-dependent potentials.
    J. Math. Phys. 32 (1991), no. 10, 2786-2801.
    [MR1130552 (93b:34107)] [Zbl 0758.35055].

  69. T. Aktosun and C. van der Mee.
    Solution of the inverse scattering problem for the three dimensional Schrödinger equation using a Fredholm integral equation.
    SIAM J. Math. Anal. 22 (1991), no. 3, 717-731.
    [MR1091677 (92a:81217)] [Zbl 0737.35049].

  70. T. Aktosun and C. van der Mee.
    Wiener-Hopf factorization in the inverse scattering theory for the n-D Schrödinger equation.
    In: H. Bart, I. Gohberg, and M. A. Kaashoek (eds.),
    Topics in matrix and operator theory,

    Oper. Theory Adv. Appl., Vol. 50,
    Birkhäuser, Basel, 1991, pp. 1-21.
    [MR1115022 (92f:35050)] [Zbl 0739.35056].

  71. T. Aktosun and C. van der Mee.
    Scattering for the 1-D Schrödinger equation with energy-dependent potentials and the recovery of the potential from the reflection coefficient.
    Phys. Rev. Lett. 65 (1990), no. 11, 1289-1293.
    [MR1069087 (92b:81211)] [Zbl 1050.81706].

  72. T. Aktosun and C. van der Mee.
    Inverse scattering problem for the 3-D Schrödinger equation and Wiener-Hopf factorization of the scattering operator.
    J. Math. Phys. 31 (1990), no. 9, 2172-2180.
    [MR1067836 (92c:35120)] [Zbl 0724.47043].

  73. T. Aktosun and C. van der Mee.
    Multidimensional inverse quantum scattering problem and Wiener-Hopf factorization.
    In: P. C. Sabatier (ed.),
    Inverse methods in action,

    Springer, Berlin, 1990, pp. 239-245.
    [MR1107970].

  74. T. Aktosun and C. van der Mee.
    Construction of the potential of the 3-D Schrödinger equation from the scattering operator by using a Fredholm integral equation.
    Phys. Rev. Lett. 63 (1989), no. 23, 2541-2543.
    [MR1025449 (90k:81258)].

  75. T. Aktosun and C. van der Mee.
    Existence of the Jost operator and solution of the 3-D inverse scattering problem by Wiener-Hopf factorization.
    Phys. Rev. Lett. 63 (1989), no. 7, 697-699.
    [MR1009538 (90h:81196)].

  76. T. Aktosun.
    Exact solutions of the Schrödinger equation and the nonuniqueness of inverse scattering on the line.
    Inverse Problems 4 (1988), no. 2, 347-352.
    [MR0954897 (89j:81232)] [Zbl 0645.34019].

  77. T. Aktosun.
    Marchenko inversion for perturbations. II: Inclusion of bound states.
    Inverse Problems 3 (1987), no. 4, 565-575.
    [MR0928045 (90e:81256b)] [Zbl 0641.35069].

  78. T. Aktosun.
    Stability of the Marchenko inversion.
    Inverse Problems 3 (1987), no. 4, 555-563.
    [MR0928044 (90d:81126)] [Zbl 0641.35070].

  79. T. Aktosun.
    Marchenko inversion for perturbations. I.
    Inverse Problems 3 (1987), no. 4, 523-553.
    [MR0928043 (90e:81256a)] [Zbl 0641.35068].

  80. T. Aktosun.
    Potentials which cause the same scattering at all energies in one dimension.
    Phys. Rev. Lett. 58 (1987), no. 21, 2159-2161.
    [MR0888716 (89f:81223)].

  81. T. Aktosun.
    An integral expression for the Jost matrix of the nonrelativistic quantum scattering on the line.
    Inverse Problems 3 (1987), no. 1, L5-L7.
    [MR0875309 (88a:81195)] [Zbl 0625.35075].

  82. T. Aktosun.
    Examples of non-uniqueness in one-dimensional inverse scattering for which T(k)=O(k3) and O(k4) as k -> 0.
    Inverse Problems 3 (1987), no. 1, L1-L3.
    [MR0875308 (88c:81115)] [Zbl 0625.35074].

  83. T. Aktosun and R. G. Newton.
    Non-uniqueness in the one-dimensional inverse scattering problem.
    Inverse Problems 1 (1985), no. 4, 291-300.
    [MR0824131 (87g:81125)] [Zbl 0602.47036].



Tuncay Aktosun aktosun@uta.edu
Last modified: August 4, 2015