Skip to main content
SpringerLink
Log in

Blowing up solutions of the modified Novikov-Veselov equation and minimal surfaces

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We propose a construction of blowup solutions of the modified Novikov-Veselov equation based on the Moutard transformation of the two-dimensional Dirac operators and on its geometric interpretation in terms of surface geometry. We consider an explicit example of such a solution constructed using the minimal Enneper surface.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. A. Taimanov, Math. Notes, 97, 126–138 (2015); arXiv:1408.4464v1 [math.DG] (2014).

    Article  Google Scholar 

  2. D. Yu, Q. P. Liu, and S. Wang, J. Phys. A: Math. Gen., 35, 3779–3785 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  3. L. V. Bogdanov, Theor. Math. Phys., 70, 219–223 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. P. Veselov and S. P. Novikov, Sov. Math. Dokl., 30, 588–591 (1984).

    MATH  Google Scholar 

  5. A. P. Veselov and S. P. Novikov, Sov. Math. Dokl., 30, 705–708 (1984).

    MATH  Google Scholar 

  6. I. A. Taimanov and S. P. Tsarev, Theor. Math. Phys., 157, 1525–1541 (2008); arXiv:0801.3225v2 [math-ph] (2008).

    Article  MATH  MathSciNet  Google Scholar 

  7. I. A. Taimanov and S. P. Tsarev, Dokl. Math., 77, 467–468 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  8. I. A. Taimanov, “Modified Novikov-Veselov equation and differential geometry of surfaces,” in: Solitons, Geometry, and Topology: On the Crossroad (AMS Transl., Ser. 2, Vol. 179, Adv. Math. Sci/., Vol. 33, V. M. Buchstaber and S. P. Novikov, eds.), Amer. Math. Soc., Providence, R. I. (1997), pp. 133–151; arXiv:dg-ga/9511005v5 (1995).

    Google Scholar 

  9. B. G. Konopelchenko, Stud. Appl. Math., 96, 9–51 (1996).

    MATH  MathSciNet  Google Scholar 

  10. I. A. Taimanov, Russ. Math. Surveys, 61, 79–159 (2006).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. T. Lamm and H. T. Nguyen, “Branched Willmore spheres,” J. Reine Angew. Math. (on-line first 2013).

    Google Scholar 

  12. I. A. Taimanov, Proc. Steklov Inst. Math., 225, 322–343 (1999).

    MathSciNet  Google Scholar 

  13. C. Bohle and G. P. Peters, Trans. Amer. Math. Soc., 363, 5419–5463 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  14. I. A. Taimanov, “A fast decaying solution to the modified Novikov-Veselov equation with a one-point singularity,” arXiv:1408.4723v2 [math.AP] (2014).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Novosibirsk, Russia

    I. A. Taimanov

  2. Novosibirsk State University, Novosibirsk, Russia

    I. A. Taimanov

Authors
  1. I. A. Taimanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Taimanov.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 182, No. 2, pp. 213–222, February, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Taimanov, I.A. Blowing up solutions of the modified Novikov-Veselov equation and minimal surfaces. Theor Math Phys 182, 173–181 (2015). https://doi.org/10.1007/s11232-015-0255-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-015-0255-5

Keywords

Search

Navigation