Talk:Inverse scattering transform

If, "It is extremely important that the eigenvalue λ be independent of time", then what does, "Step 3. Determine the time evolution of the eigenvalues λ..." mean?

This article is incomprehensible rubbish, shouldn't it be better to take it away completely. Bas Michielsen 15:42, 10 August 2007 (UTC)
 * Hello, please don't take it away. I studied that method during my studies, and though it lacks a complete example, it is quite a good start.Klinfran (talk) 08:44, 5 July 2020 (UTC)

This article is certainly poorly written. Some changes have been made to the first paragraphs but the section "Method of solution" requires a complete rewrite: still to be done. —Preceding unsigned comment added by ComtedeMonteCristo (talk • contribs) 08:07, 26 June 2008 (UTC)

Name of Article and Content
I believe this article should be renamed to Scattering Transform or Nonlinear Fourier Transform. One usually only calls the step Scattering Data -> Solution inverse scaterring. The article also requires major rewriting! E.g. scattering data as the reflection coefficient is completely missing, and also that it then solves linear odes!

ElMaison (talk) 03:29, 31 March 2008 (UTC)

Revision
I have created a major revision for this article. If you disagree, then let us discuss and revise as needed, but please do not revert the article as there are many deficiencies with the current article. I retained as much of the current content as feasible. Reasons for revision:
 * I added citations to reliable secondary and tertiary sources; the current content lacks reliable citations.
 * I added a diagram showing the basic algorithm
 * I added a description of the algorithm in the introduction; current article does not define the algortithm in the introduction.
 * I added a clear explanation of the method and example, current article description is unclear, incomplete and contains non-relevant content.
 * Removed content that was not appropriate.

Removed content: TMM53 (talk) 01:09, 28 March 2024 (UTC)
 * Unnecessary verbiage e.g. "so called," "that is to say," "it should be the case that"
 * Not encyclopedic content as not seen in major introductory textbooks or review artices and not sourced e.g "the Bogomolny equations (for a given gauge group and oriented Riemannian 3-fold), the solutions of which are magnetic monopoles."
 * Conflicts with what Ambowitz states and is unexplained i.e. How did this arise from nonlinear optics? e.g. "The term "soliton" arises from non-linear optics."
 * Does not belong in introduction; introduction content must be easy to understand e.g. "completely integrable infinite dimensional systems."
 * Does not belong in introduction, unsourced and unexplained, introductory content must be the simplest content e.g. "The inverse scattering problem can be written as a Riemann–Hilbert factorization problem, at least in the case of equations of one space dimension. This formulation can be generalized to differential operators of order greater than 2 and also to periodic potentials. In higher space dimensions one has instead a "nonlocal" Riemann–Hilbert factorization problem (with convolution instead of multiplication) or a d-bar problem"
 * Unsourced e.g. "This step works if is a differential or difference operator of order two, but not necessarily for higher orders."
 * Requesting the reader to look some where else for information; if information is usefull and appropriate then summarize and put in article e.g. "See Ablowitz-Clarkson (1991) for either approach. See Marchenko (1986) for a mathematical rigorous treatment"
 * Unexplained equation, why is this relevant? $$ \psi_t + \psi_{xxx} -3(u-\lambda) \psi_x = C\psi+D\psi\int \frac{1}{\psi^2} dx$$
 * Unclear what does this means? Needs a better explanation. "Comparing the expression $$L_t v + L v_t$$ with $$\partial_t \left(v_{xx} +uv\right)$$ shows us that $$L_t = u_t,$$ thus ignoring the first term."


 * I made the revision.TMM53 (talk) 01:12, 28 March 2024 (UTC)