Skip to main content

Relation between Bäcklund transformations and inverse scattering problems

  • Conference paper
  • First Online:
Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

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.

    Article  MathSciNet  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  Google Scholar 

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

    Article  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.

    Article  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

Robert M. Miura

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

Publish with us

Policies and ethics