General derivation of Baecklund transformations from inverse scattering problems Page: 4 of 12
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
-2-
1
Recently, Ablowitz et. al. discovered a general scheme of finding
the set of nonlinear partial differential equations that are solvable by
inverse scattering method. We will show in this paper how one can
derive the Backlund transformation from the auxiliary equations for the
inverse problem. 2 This derivation provides the basis of unifying the two
different approaches of solving these non-linear equations.
1. Equations solvable by inverse method.
1
Ablowitz et. al. have found that the integrability conditions for
the systems of linear partial differential equationsvx + i v1 = qv2
v2x -iv =rv1and
(1)
are exactly those equations
inverse scattering method.vlt = Av1 + Bv2
v2t = Cvl - Avg
which allow soliton solutions solvable by
The integrability conditions are:A = qC - rB
B + 2i B - q - ZAq
x t
C- 2irC =r + ZAr .(2)
(3)Finite expansions of A, B and C in terms of reduces it to specific
equations of interest. For example, KdV , rnKdV 3, sine-Gordon and
nonlinear Schrodinger equation. 5
Upcoming Pages
Here’s what’s next.
Search Inside
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Chen, H.H. General derivation of Baecklund transformations from inverse scattering problems, report, August 1, 1974; United States. (https://digital.library.unt.edu/ark:/67531/metadc1019785/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.