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Journal articles on the topic 'Inverse Scattering Transform'

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Published: 4 June 2021

Last updated: 24 January 2023

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1

Steudel, H., and D. J. Kaup. "Inverse scattering transform on a finite interval." Journal of Physics A: Mathematical and General 32, no. 34 (August 13, 1999): 6219–31. http://dx.doi.org/10.1088/0305-4470/32/34/308.

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2

Vekslerchik, V. E. "Inverse scattering transform for the nonlinear -model." Inverse Problems 12, no. 4 (August 1, 1996): 517–34. http://dx.doi.org/10.1088/0266-5611/12/4/012.

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3

Desbruslais, Stephen. "Inverse Scattering Transform for Soliton Transmission Analysis." Optical Fiber Technology 2, no. 4 (October 1996): 319–42. http://dx.doi.org/10.1006/ofte.1996.0037.

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4

Teschl, Gerald. "Inverse Scattering Transform for the Toda Hierarchy." Mathematische Nachrichten 202, no. 1 (1999): 163–71. http://dx.doi.org/10.1002/mana.19992020113.

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5

Fokas, A. S. "Inverse scattering transform, inverse data and nonlinear evolution equations in multidimensions." Physica D: Nonlinear Phenomena 28, no. 1-2 (September 1987): 223. http://dx.doi.org/10.1016/0167-2789(87)90145-x.

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6

Cable, J. R., and A. C. Albrecht. "A direct inverse transform for resonance Raman scattering." Journal of Chemical Physics 84, no. 9 (May 1986): 4745–54. http://dx.doi.org/10.1063/1.449958.

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7

Turitsyna, Elena G., and Sergei K. Turitsyn. "Digital signal processing based on inverse scattering transform." Optics Letters 38, no. 20 (October 11, 2013): 4186. http://dx.doi.org/10.1364/ol.38.004186.

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8

Constantin, Adrian, Rossen I. Ivanov, and Jonatan Lenells. "Inverse scattering transform for the Degasperis–Procesi equation." Nonlinearity 23, no. 10 (August 20, 2010): 2559–75. http://dx.doi.org/10.1088/0951-7715/23/10/012.

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9

Constantin, Adrian, Vladimir S. Gerdjikov, and Rossen I. Ivanov. "Inverse scattering transform for the Camassa–Holm equation." Inverse Problems 22, no. 6 (October 20, 2006): 2197–207. http://dx.doi.org/10.1088/0266-5611/22/6/017.

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10

Villarroel, J. "Yang-Mills equations and the inverse scattering transform." Journal of Physics A: Mathematical and General 24, no. 15 (August 7, 1991): 3587–92. http://dx.doi.org/10.1088/0305-4470/24/15/025.

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11

Osborne, A. R. "Soliton physics and the periodic inverse scattering transform." Physica D: Nonlinear Phenomena 86, no. 1-2 (September 1995): 81–89. http://dx.doi.org/10.1016/0167-2789(95)00089-m.

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12

Yan, Chuntao. "Regularized long wave equation and inverse scattering transform." Journal of Mathematical Physics 34, no. 6 (June 1993): 2618–30. http://dx.doi.org/10.1063/1.530087.

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13

Chun-Nuan, Yang, Yu Jia-Lu, Wang Qu-Quan, and Huang Nian-Ning. "Demonstration of Inverse Scattering Transform for DNLS Equation." Communications in Theoretical Physics 48, no. 2 (August 2007): 299–303. http://dx.doi.org/10.1088/0253-6102/48/2/019.

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14

Buonocore, Michael H. "RF pulse design using the inverse scattering transform." Magnetic Resonance in Medicine 29, no. 4 (April 1993): 470–77. http://dx.doi.org/10.1002/mrm.1910290408.

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15

Gerdjikov, V. S., and N. A. Kostov. "Inverse scattering transform analysis of Stokes–anti-Stokes stimulated Raman scattering." Physical Review A 54, no. 5 (November 1, 1996): 4339–50. http://dx.doi.org/10.1103/physreva.54.4339.

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16

Wang, Xueru, and Junyi Zhu. "Broer-Kaup System with Corrections via Inverse Scattering Transform." Advances in Mathematical Physics 2020 (September 15, 2020): 1–11. http://dx.doi.org/10.1155/2020/7859897.

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The Broer-Kaup system with corrections is considered. Based on the inverse scattering transform, we extend the perturbation theory to discuss the adiabatic approximate solution and ε-order approximate solution of one soliton to the Broer-Kaup system with corrections.

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17

Joo, Taiha, and A. C. Albrecht. "Inverse transform in resonance Raman scattering: an iterative approach." Journal of Physical Chemistry 97, no. 7 (February 1993): 1262–64. http://dx.doi.org/10.1021/j100109a004.

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18

Kaup, D. J., and Y. Matsuno. "The Inverse Scattering Transform for the Benjamin–Ono Equation." Studies in Applied Mathematics 101, no. 1 (July 1998): 73–98. http://dx.doi.org/10.1111/1467-9590.00086.

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19

Epstein, Charles L. "Minimum energy pulse synthesis via the inverse scattering transform." Journal of Magnetic Resonance 167, no. 2 (April 2004): 185–210. http://dx.doi.org/10.1016/j.jmr.2003.12.014.

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20

Magland, Jeremy, and Charles L. Epstein. "Exact half pulse synthesis via the inverse scattering transform." Journal of Magnetic Resonance 171, no. 2 (December 2004): 305–13. http://dx.doi.org/10.1016/j.jmr.2004.09.004.

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21

Magland, Jeremy, and Charles L. Epstein. "Practical pulse synthesis via the discrete inverse scattering transform." Journal of Magnetic Resonance 172, no. 1 (January 2005): 63–78. http://dx.doi.org/10.1016/j.jmr.2004.09.022.

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22

Shailaja, R., and M. J. Vedan. "Inverse Scattering Transform (IST) analysis of KdV-burgers' equation." International Journal of Non-Linear Mechanics 30, no. 5 (September 1995): 617–27. http://dx.doi.org/10.1016/0020-7462(95)00028-m.

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23

Chun-Nuan, Yang, Yu Jia-Lu, Cai Hao, and Huang Nian-Ning. "Inverse Scattering Transform for the Derivative Nonlinear Schrödinger Equation." Chinese Physics Letters 25, no. 2 (February 2008): 421–24. http://dx.doi.org/10.1088/0256-307x/25/2/019.

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24

Kawata, Tsutomu. "Inverse Scattering Transform of the Higher-Order Eigenvalue Problem." Journal of the Physical Society of Japan 57, no. 2 (February 15, 1988): 422–35. http://dx.doi.org/10.1143/jpsj.57.422.

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25

Shimizu, Koichi, and Akira Ishimaru. "Differential Fourier transform technique for the inverse scattering problem." Applied Optics 29, no. 23 (August 10, 1990): 3428. http://dx.doi.org/10.1364/ao.29.003428.

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26

Yin, Tiantian, Zhun Wei, and Xudong Chen. "Wavelet Transform Subspace-Based Optimization Method for Inverse Scattering." IEEE Journal on Multiscale and Multiphysics Computational Techniques 3 (2018): 176–84. http://dx.doi.org/10.1109/jmmct.2018.2878483.

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27

Power, J. F. "Inverse scattering theory of Fourier transform infrared photoacoustic spectroscopy." Analyst 121, no. 4 (1996): 451. http://dx.doi.org/10.1039/an9962100451.

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28

Fokas, A. S., and M. J. Ablowitz. "Forced Nonlinear Evolution Equations and the Inverse Scattering Transform." Studies in Applied Mathematics 80, no. 3 (June 1989): 253–72. http://dx.doi.org/10.1002/sapm1989803253.

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29

Lipovsky, V. D., and A. V. Shirokov. "Inverse scattering transform method for the Zakharov-Manakov system." Journal of Mathematical Sciences 83, no. 1 (January 1997): 93–105. http://dx.doi.org/10.1007/bf02398464.

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30

Bernstein, Swanhild. "The Schrödinger equation and a multidimensional inverse scattering transform." Mathematical Methods in the Applied Sciences 25, no. 16-18 (November 10, 2002): 1343–53. http://dx.doi.org/10.1002/mma.374.

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31

Fustero, Xavier, and Enric Verdaguer. "Einstein-Rosen metrics generated by the inverse scattering transform." General Relativity and Gravitation 18, no. 11 (November 1986): 1141–58. http://dx.doi.org/10.1007/bf00763540.

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32

Konopelchenko, B. G., and B. T. Matkarimov. "On the inverse scattering transform for the Ishimori equation." Physics Letters A 135, no. 3 (February 1989): 183–89. http://dx.doi.org/10.1016/0375-9601(89)90259-4.

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33

Xin, Z. "Inverse Scattering Transform for Systems with Rational Spectral Dependence." Journal of Differential Equations 115, no. 2 (January 1995): 277–303. http://dx.doi.org/10.1006/jdeq.1995.1015.

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34

Zhang, Sheng, and Caihong You. "Inverse scattering transform for a supersymmetric Korteweg-de Vries equation." Thermal Science 23, Suppl. 3 (2019): 677–84. http://dx.doi.org/10.2298/tsci180512081z.

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In this paper, the inverse scattering transform is extended to a super Korteweg-de Vries equation with an arbitrary variable coefficient by using Kulish and Zeitlin?s approach. As a result, exact solutions of the super Korteweg-de Vries equation are obtained. In the case of reflectionless potentials, the obtained exact solutions are reduced to soliton solutions. More importantly, based on the obtained results, an approach to extending the scattering transform is proposed for the supersymmetric Korteweg-de Vries equation in the 1-D Grassmann algebra. It is shown the the approach can be applied to some other supersymmetric non-linear evolution equations in fluids.

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35

Tirozzi, Brunello. "Scattering of Lower Hybrid Waves in a Magnetized Plasma." Physics 2, no. 4 (November 29, 2020): 640–53. http://dx.doi.org/10.3390/physics2040037.

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In this paper, the Maxwell equations for the electric field in a cold magnetized plasma in the half-space of x≥0 cm are solved. The boundary conditions for the electric field include a pointwise source at the plane x=0 cm, the derivatives of the electric field that are zero statV/cm2 at x=0 cm, and the field with all its derivatives that are zero at infinity. The solution is explored in terms of the Laplace transform in x and the Fourier transform in y-z directions. The expressions of the field components are obtained by the inverse Laplace transform and the inverse Fourier transform. The saddle-point technique and power expansion have been used for evaluating the inverse Fourier transform. The model represents the propagation of a lower hybrid wave generated by a pointwise antenna located at the boundary of the plasma. Here, the antenna is the boundary condition. The validation of the model is performed assuming that the electric field component Ey=0 statV/cm and by comparing it with the model of electromagnetic waves generated by a local small antenna located near the boundary of a tokamak, and an experiment is suggested.

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36

Wieder, Thomas. "A Generalized Debye Scattering Formula and the Hankel Transform." Zeitschrift für Naturforschung A 54, no. 2 (February 1, 1999): 124–30. http://dx.doi.org/10.1515/zna-1999-0206.

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Abstract The diffracted intensity of an x-ray or neutron diffraction experiment is expressed as an integral over an atomic position distribution function. A generalized Debye scattering formula results. Since this distribution function is expanded into a series of spherical harmonics, an inverse Hankel transform of the intensity allows the calculation of the expansion coefficients which describe the atomic arrangement completely. The connections between the generalized Debye scattering formula and the original Debye formula as well as the Laue scattering formula are derived.

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37

Fang, Fang, Beibei Hu, and Ling Zhang. "Inverse Scattering Transform for the Generalized Derivative Nonlinear Schrödinger Equation via Matrix Riemann–Hilbert Problem." Mathematical Problems in Engineering 2022 (April 26, 2022): 1–9. http://dx.doi.org/10.1155/2022/3967328.

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The inverse scattering transformation for a generalized derivative nonlinear Schrödinger (GDNLS) equation is studied via the Riemann–Hilbert approach. In the direct scattering process, we perform the spectral analysis of the Lax pair associated with a 2 × 2 matrix spectral problem for the GDNLS equation. Then, the corresponding Riemann–Hilbert problem is constructed. In the inverse scattering process, we obtain an N-soliton solution formula for the GDNLS equation by solving the Riemann–Hilbert problem with the reflection-less case. In addition, we express the N-soliton solution of the GDNLS equation as determinant expression.

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38

Fang, Fang, Beibei Hu, and Ling Zhang. "Inverse Scattering Transform for the Generalized Derivative Nonlinear Schrödinger Equation via Matrix Riemann–Hilbert Problem." Mathematical Problems in Engineering 2022 (April 26, 2022): 1–9. http://dx.doi.org/10.1155/2022/3967328.

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The inverse scattering transformation for a generalized derivative nonlinear Schrödinger (GDNLS) equation is studied via the Riemann–Hilbert approach. In the direct scattering process, we perform the spectral analysis of the Lax pair associated with a 2 × 2 matrix spectral problem for the GDNLS equation. Then, the corresponding Riemann–Hilbert problem is constructed. In the inverse scattering process, we obtain an N-soliton solution formula for the GDNLS equation by solving the Riemann–Hilbert problem with the reflection-less case. In addition, we express the N-soliton solution of the GDNLS equation as determinant expression.

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39

Zimmerman, W. B., and G. W. Haarlemmer. "Internal gravity waves: Analysis using the periodic, inverse scattering transform." Nonlinear Processes in Geophysics 6, no. 1 (March 31, 1999): 11–26. http://dx.doi.org/10.5194/npg-6-11-1999.

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Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s) * (ε/μ2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.

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40

Gkogkou, Aikaterini, Barbara Prinari, Bao‐Feng Feng, and A. David Trubatch. "Inverse scattering transform for the complex coupled short‐pulse equation." Studies in Applied Mathematics 148, no. 2 (October 26, 2021): 918–63. http://dx.doi.org/10.1111/sapm.12463.

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41

Ma, Xinxin, and Yonghui Kuang. "Inverse scattering transform for a nonlocal derivative nonlinear Schrödinger equation." Theoretical and Mathematical Physics 210, no. 1 (January 2022): 31–45. http://dx.doi.org/10.1134/s0040577922010032.

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42

Grinevich, P. G., and P. M. Santini. "Nonlocality and the Inverse Scattering Transform for the Pavlov Equation." Studies in Applied Mathematics 137, no. 1 (April 1, 2016): 10–27. http://dx.doi.org/10.1111/sapm.12127.

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43

Ablowitz, Mark J., and Ziad H. Musslimani. "Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation." Nonlinearity 29, no. 3 (February 4, 2016): 915–46. http://dx.doi.org/10.1088/0951-7715/29/3/915.

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44

Sabatier, P. C. "Generalized inverse scattering transform applied to linear partial differential equations." Inverse Problems 22, no. 1 (January 13, 2006): 209–28. http://dx.doi.org/10.1088/0266-5611/22/1/012.

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45

Biondini, Gino, Ildar Gabitov, Gregor Kovačič, and Sitai Li. "Inverse scattering transform for two-level systems with nonzero background." Journal of Mathematical Physics 60, no. 7 (July 2019): 073510. http://dx.doi.org/10.1063/1.5084720.

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46

Cheney, Margaret, and James H. Rose. "Generalization of the Fourier transform: Implications for inverse scattering theory." Physical Review Letters 60, no. 13 (March 28, 1988): 1221–24. http://dx.doi.org/10.1103/physrevlett.60.1221.

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47

Novikov, S. P., and A. P. Veselov. "Two-dimensional Schrödinger operator: Inverse scattering transform and evolutional equations." Physica D: Nonlinear Phenomena 18, no. 1-3 (January 1986): 267–73. http://dx.doi.org/10.1016/0167-2789(86)90187-9.

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48

Pogrebkov, A. K. "Hirota difference equation: Inverse scattering transform, darboux transformation, and solitons." Theoretical and Mathematical Physics 181, no. 3 (December 2014): 1585–98. http://dx.doi.org/10.1007/s11232-014-0237-z.

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49

Butler, Samuel, and Nalini Joshi. "An inverse scattering transform for the lattice potential KdV equation." Inverse Problems 26, no. 11 (October 5, 2010): 115012. http://dx.doi.org/10.1088/0266-5611/26/11/115012.

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50

Tchokouansi, Hermann T., Victor K. Kuetche, and Timoleon C. Kofane. "Inverse scattering transform of a new optical short pulse system." Journal of Mathematical Physics 55, no. 12 (December 2014): 123511. http://dx.doi.org/10.1063/1.4904492.

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