Skip to main content

Relation between Bäcklund transformations and inverse scattering problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 515)

Keywords

  • Soliton Solution
  • Nonlinear Evolution Equation
  • Nonlinear Partial Differential Equation
  • Scattering Problem
  • MKdV Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.C. SCOTT, F.Y.F. CHU, AND D.W. MCLAUGHLIN, The soliton: A new concept in applied science, Proc. IEEE 61 (1973), 1443–1483.

    CrossRef  MathSciNet  Google Scholar 

  2. P.D. LAX, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968), 647–690.

    CrossRef  MathSciNet  Google Scholar 

  3. I.M. GEL’FAND AND B.M. LEVITAN, On the determination of a differential equation from its spectral function, Amer. Math. Soc. Trans. Ser. 2 1 (1955), 253–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. C.S. GARDNER, J.M. GREENE, M.D. KRUSKAL, AND R.M. MIURA, Method for solving the Korteweg-deVries equation, Phys. Rev. Lett. 19 (1967), 1095–1097; Korteweg-deVries equation and generalizations. VI. Methods for exact solution, Comm. Pure Appl. Math. 27 (1974), 97–133.

    CrossRef  MATH  Google Scholar 

  5. G.L. LAMB, JR., Analytical descriptions of ultrashort optical pulse propagation in a resonant medium, Rev. Modern Phys. 43 (1971), 99–124.

    CrossRef  MathSciNet  Google Scholar 

  6. H.D. WAHLQUIST AND F.B. ESTABROOK, Bäcklund transformation for solutions of the Korteweg-deVries equation, Phys. Rev. Lett. 31 (1973), 1386–1390.

    CrossRef  MathSciNet  Google Scholar 

  7. H.-H. CHEN, General derivation of Bäcklund transformations from inverse scattering problems, Phys. Rev. Lett. 33 (1974), 925–928.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. M.J. ABLOWITZ, D.J. KAUP, A.C. NEWELL, AND H. SEGUR, Nonlinear-evolution equations of physical significance, Phys. Rev. Lett. 31 (1973), 125–127; The inverse scattering transform—Fourier analysis for nonlinear problems, Studies in Appl. Math. 53 (1974), 249–315.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. V.E. ZAKHAROV, On stochastization of one-dimensional chains of nonlinear oscillators, Soviet Physics JETP 38 (1974), 108–110.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Chen, HH. (1976). Relation between Bäcklund transformations and inverse scattering problems. In: Miura, R.M. (eds) Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications. Lecture Notes in Mathematics, vol 515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081171

Download citation

  • DOI: https://doi.org/10.1007/BFb0081171

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07687-2

  • Online ISBN: 978-3-540-38220-1

  • eBook Packages: Springer Book Archive