Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

Request Permissions   Purchase Content 


Scattering problem for the ordinary differential operator of order four on the half-line. I. Direct problem

Authors: R. Shterenberg and V. Sukhanov
Translated by: the author
Original publication: Algebra i Analiz, tom 25 (2013), nomer 2.
Journal: St. Petersburg Math. J. 25 (2014), 327-337
MSC (2010): Primary 34L25
Published electronically: March 12, 2014
MathSciNet review: 3114857
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Direct and inverse spectral problems are studies for ordinary differential operators of order four on the half-line. This first part of the text is devoted to the study of the direct problem.

References [Enhancements On Off] (What's this?)

  • 1. R. Beals, P. Deift, and C. Tomei, Direct and inverse scattering on the line, Math. Surveys Monogr., vol. 28, Amer. Math. Soc., Providence, RI, 1988. MR 954382 (90a:58064)
  • 2. P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), no. 2, 121-251. MR 512420 (80e:34011)
  • 3. P. Deift and X. Zhou, Direct and inverse scattering on the line with arbitrary singularities, Comm. Pure Appl. Math. 44 (1991), no. 5, 485-533. MR 1105873 (92g:34112)
  • 4. V. V. Sukhanov, An inverse problem for a selfajoint operator on the axis, Mat. Sb. (N.S.) 137 (1988), no. 2, 242-259; English transl., Math. USSR-Sb. 65 (1990), no. 1, 249-266. MR 971696 (89k:34036)
  • 5. J. Östensson, Trace formulae and spectral properties of fourth order differential operators, KTH, PhD-thesis.
  • 6. A. Laptev, R. Shterenberg, V. Sukhanov, and J. Östensson, Reflectionless potentials for an ordinary differential operator of order four, Inverse Problems 22 (2006), no. 1, 135-153. MR 2194188 (2006k:34230)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 34L25

Retrieve articles in all journals with MSC (2010): 34L25

Additional Information

R. Shterenberg
Affiliation: Department of Mathematics, University of Alabama at Birmingham, 1300 University Blvd, Birmingham, Alabama 35294

V. Sukhanov
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 3, Petrodvorets, St. Petersburg 185504, Russia

Keywords: Ordinary differential operator, scattering problem on the half-axis, inverse problem, operator of order four.
Received by editor(s): November 5, 2012
Published electronically: March 12, 2014
Additional Notes: Supported by RFBR (grant no. 05-01-01076)
Dedicated: Dedicated to the memory of V. S. Buslaev
Article copyright: © Copyright 2014 American Mathematical Society

American Mathematical Society