Skip to main content
SpringerLink
Log in

Soliton Solutions as Inverse Problem for Coefficient Identification

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8353))

Included in the following conference series:

  • 1294 Accesses

Abstract

We construct an algorithm to investigate numerically non-symmetric solitary wave-like solutions of an ordinary nonlinear differential equation. We reformulate the bifurcation problem, introducing a new parameter; and in such a way we expel the trivial solution of the original problem. The Method of Variational Imbedding (MVI) is used for solving the inverse problem. We illustrate the approach by comparing the numerical solution with a known exact solution of the Boussinesq equation.

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

Access this chapter

Log in via an institution
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 EPUB and 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

References

  1. Boussinesq, J.: Theorie de l’intumescence liquide appelee onde solitaire ou de translation se propageant dans un canal rectangulare. C. R. Acad. Sci. 72, 755–759 (1871)

    MATH  Google Scholar 

  2. Camassa, R., Holm, D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett 71(11), 1661–1664 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Marinov, T.T., Christov, C.I., Marinova, R.S.: Novel numerical approach to solitary-wave solutions identification of Boussinesq and Korteweg-de Vries equations. Int. J. Bifurcat. Chaos 15(2), 557–565 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lenells, J.: Traveling wave solutions of the Camassa-Holm equation. J. Differ. Equ. 217, 393–430 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Russell, J.S.: Report on waves. 14th Meeting of the British Association Report, York (1844)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Natural Sciences, Southern University at New Orleans, 6801 Press Drive, New Orleans, LA, 70126, USA

    Tchavdar T. Marinov

  2. Department of Mathematical and Computing Sciences, Concordia University College of Alberta, Edmonton, AB, T5B 4E4, Canada

    Rossitza Marinova

Authors
  1. Tchavdar T. Marinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rossitza Marinova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rossitza Marinova .

Editor information

Editors and Affiliations

  1. Inst. of Info. & Comm. Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

  3. Dept. of Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marinov, T.T., Marinova, R. (2014). Soliton Solutions as Inverse Problem for Coefficient Identification. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43880-0_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43879-4

  • Online ISBN: 978-3-662-43880-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation