scattering.: 4960  The direct scattering transform describes how a function scatters waves or generates bound-states.: 39–43  The inverse scattering transform...

and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation...

Martin Kruskal and Norman Zabusky in 1965, which led to the inverse scattering transform method in 1967. In the special case of Hamiltonian systems, if...

needed] An important concept in the inverse scattering transform is the Lax representation. The quantum inverse scattering method starts by the quantization...

introduced by Peter Lax to discuss solitons in continuous media. The inverse scattering transform makes use of the Lax equations to solve such systems. A Lax pair...

Chirplet transform Distance transform Fractal transform Gelfand transform Hadamard transform Hough transform (digital image processing) Inverse scattering transform...

Zabusky and Kruskal in 1965 and then the development of the inverse scattering transform in 1967. In 1972, T. Kawahara proposed a fifth-order KdV type...

The Belinski–Zakharov transform is a generalization of the inverse scattering transform. The solutions produced by this transform are called gravitational...

as breather solutions. It can be solved exactly by use of the inverse scattering transform, as shown by Zakharov & Shabat (1972) (see below). The other...

left and right halves of the result of the transform. The inverse transform is given by: Inverse transform Eq.2. is also N {\displaystyle N} -periodic...

connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays (electron...

Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts...

The soliton solutions are typically obtained by means of the inverse scattering transform, and owe their stability to the integrability of the field equations...

the Kadomtsev–Petviashvili equation, it is integrable via the inverse scattering transform for the 2-dimensional stationary Schrödinger equation. Similarly...

function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included...

one class of nonlinear inverse problems was so before 1970, that of inverse spectral and (one space dimension) inverse scattering problems, after the seminal...

equation is completely integrable. It can also be solved using the inverse scattering transform much like the nonlinear Schrödinger equation. In 2002, the regularized...

coordinate x and time t. An exact solution found by using the inverse scattering transform is: u = 4 arctan ⁡ ( 1 − ω 2 cos ⁡ ( ω t ) ω cosh ⁡ ( 1 − ω 2...

ISBN 978-1-4214-1079-1. Alfred Osborne (2010). Nonlinear Ocean Waves & the Inverse Scattering Transform. Academic Press. ISBN 978-0-08-092510-3. Michael E. McCormick...

In chemistry and physics, Raman scattering or the Raman effect (/ˈrɑːmən/) is the inelastic scattering of photons by matter, meaning that there is both...

overview of nonlinear water waves". Nonlinear Ocean Waves and the Inverse Scattering Transform. Academic Press. pp. 3 ff. ISBN 978-0-12-528629-9. Alexander...

the 2D planar Inverse ISAR transform include: Image blocking modeling errors: The Inverse ISAR transform currently assumes that scatterers are on a planar...

allows for exact analytical solutions via methods such as the inverse scattering transform, making them a cornerstone in the mathematical theory of integrable...

Mie scattering, so this would infer that it should be less than 5 μm for mid-infrared spectroscopy. The spectra are plotted in units of log inverse reflectance...

theory, an axiomatic basis for part of non-standard analysis Inverse scattering transform, a method for solving some non-linear partial differential equations...

"The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons", The sine-Gordon Model and its Applications, Nonlinear...

Fourier-transform spectroscopy principles in scanning near-field optical microscopy techniques. Particularly in nano-FTIR, where the scattering from a...

presence of solitons. Techniques for solving these include the inverse scattering transform and the method of Lax pairs, the Yang–Baxter equation and quantum...

Mark J.; Kaup, David J.; Newell, Alan C. (1974-12-01). "The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems". Studies in Applied...

(black hole entropy), Vladimir A. Belinsky (BKL conjecture, inverse scattering transform solution generating methods), Peter G. Bergmann (constrained...