Skip to main content
SpringerLink
Log in

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

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

Abstract

We consider matrix solutions of a noncommutative KP and a noncommutative mKP equation; these solutions can be expressed as quasideterminants. In particular, we investigate the interaction of two-soliton solutions.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. R. Gilson, J. J. C. Nimmo, and C. M. Sooman, J. Phys. A, 41, 085202 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  2. O. Lechtenfeld, L. Mazzanti, S. Penati, A. D. Popov, and L. Tamassia, Nucl. Phys. B, 705, 477–503 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. C. X. Li and J. J. C. Nimmo, Proc. R. Soc. London Ser. A, 464, 951–966 (2008).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. A. Dimakis and F. Müller-Hoissen, J. Phys. A, 39, 9169–9186 (2006).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. N. Wang and M. Wadati, J. Phys. Soc. Japan, 73, 1689–1698 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. V. M. Goncharenko, Theor. Math. Phys., 126, 81–91 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  7. C. R. Gilson and J. J. C. Nimmo, J. Phys. A, 40, 3839–3850 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. M. Hamanaka and K. Toda, J. Phys. A, 36, 11981–11998 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. M. Hamanaka, “Noncommutative solitons and integrable systems,” in: Noncommutative Geometry and Physics (Y. Maeda, N. Tose, N. Miyazaki, S. Watamura, and D. Sternheimer, eds.), World Scientific, Hackensack, N. J. (2005), pp. 175–198.

    Google Scholar 

  10. A. Dimakis and F. Müller-Hoissen, Phys. Lett. A, 278, 139–145 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  11. B. A. Kupershmidt, KP or mKP: Noncommutative Mathematics of Lagrangian, Hamiltonian, and Integrable Systems (Math. Surveys Monogr., Vol. 78), Amer. Math. Soc., Providence, R. I. (2000).

    MATH  Google Scholar 

  12. I. M. Gelfand, S. I. Gelfand, V. S. Retakh, and R. L. Wilson, Adv. Math., 193, 56–141 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  13. V. M. Goncharenko and A. P. Veselov, J. Phys. A, 31, 5315–5326 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. V. M. Goncharenko and A. P. Veselov, “Yang-Baxter maps and matrix solitons,” in: New Trends in Integrability and Partial Solvability (NATO Sci. Ser. II Math. Phys. Chem., Vol. 132, A. B. Shabat, A. González-López, M. Mañas, L. Martínez Alonso, and M. A. Rodríguez, eds.), Kluwer, Dordrecht (2004), pp. 191–197.

    Google Scholar 

  15. V. M. Goncharenko, Russ. Math. Surveys, 55, 995–997 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  16. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991).

    MATH  Google Scholar 

  17. W. Oevel and C. Rogers, Rev. Math. Phys., 5, 299–330 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  18. J. J. C. Nimmo, “Darboux transformations from reductions of the KP hierarchy,” in: Nonlinear Evolution Equations and Dynamical Systems: NEEDS’ 94 (Los Alamos, N. Mex., V. G. Makhanov, A. R. Bishop, and D. D. Holm, eds.), World Scientific, River Edge, N. J. (1995), pp. 168–177.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Glasgow, Glasgow, UK

    C. R. Gilson, J. J. C. Nimmo & C. M. Sooman

Authors
  1. C. R. Gilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. J. C. Nimmo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. M. Sooman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. M. Sooman.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 448–458, June, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gilson, C.R., Nimmo, J.J.C. & Sooman, C.M. Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation. Theor Math Phys 159, 796–805 (2009). https://doi.org/10.1007/s11232-009-0068-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-009-0068-5

Keywords

Search

Navigation