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On Type-II Bäcklund Transformation for the MKdV Hierarchy

  • Hui Mao und Shuqiang Lv EMAIL logo
Veröffentlicht/Copyright: 11. Januar 2017

Abstract

The study of new integrable defects leads to new type of Bäcklund transformations named as the type-II Bäcklund transformations. In this article, we show, for the MKdV hierarchy, that the type-II Bäcklund transformation is the compound type-I Bäcklund transformation.

Acknowledgments

The comments of the anonymous reviewers have been useful to improve the paper. This work is supported by the National Natural Science Foundation of China (grant numbers: 11271366 and 11331008), Beijing Municipal Commission of Education Science and Technology Plan project (grant numbers: KM201511417007), the Fundamental Research Funds for Central Universities, and “New Start” Academic Research Projects of Beijing Union University (ZK10201412).

References

[1] C. Gu, H. Hu, and Z. Zhou, Darboux Transformation in Integrable Systems: Theory and Their Applications to Geometry, Springer, Dordrecht 2005.10.1007/1-4020-3088-6Suche in Google Scholar

[2] C. Rogers and W. F. Shadwick, Bäcklund Transformations and Their Applications, Academic Press, New York 1982.Suche in Google Scholar

[3] C. Rogers and W. Schief, Bäcklund and Darboux Transformations – Geoemetry and Modern Applications in Soliton Theory, Cambridge University Press, Cambridge, UK 2002.10.1017/CBO9780511606359Suche in Google Scholar

[4] D. Levi and R. Benguria, Proc. Natl. Acad. Sci. USA 77, 5025 (1980).10.1073/pnas.77.9.5025Suche in Google Scholar

[5] D. Levi, J. Phys. A: Math. Gen. 14, 1083 (1981).10.1088/0305-4470/14/5/028Suche in Google Scholar

[6] Y. B. Suris, The Problem of Integrable Discretization: Hamiltonian Approach, Birkhäuser, Basel 2003.10.1007/978-3-0348-8016-9Suche in Google Scholar

[7] P. Bowcock, E. Corrigan, and C. Zambon, Inter. J. Mod. Phys. A 19 (Supplement), 82 (2004).10.1142/S0217751X04020324Suche in Google Scholar

[8] E. Corrigan, C. Zambon, J. Phys. A: Math. Theor. 42, 475203 (2009).10.1088/1751-8113/42/47/475203Suche in Google Scholar

[9] A. R. Aguirre, J. F. Gomes, N. I. Spano, and A. H. Zimerman, J. High Energy Phys. 06, 125 (2015).10.1007/JHEP06(2015)125Suche in Google Scholar

[10] B. G. Konopelcheko and C. Rogers, in: Nonlinear Equations in Applied Sciences (Eds. W. F. Ames, C. Rogers), Academic Press, San Diego 1992.Suche in Google Scholar

[11] W. Oevel, C. Rogers, Rev. Math. Phys. 5, 299 (1993).10.1142/S0129055X93000073Suche in Google Scholar

[12] A. R. Aguirre, T. R. Araujo, J. F. Gomes, and A. H. Zimerman, J. High Energy Phys. 12, 056 (2011).10.1007/JHEP12(2011)056Suche in Google Scholar

[13] J. F. Gomes, A. L. Retore, and A. H. Zimerman, J. Phys. A: Math. Theor. 48, 405203 (2015).10.1088/1751-8113/48/40/405203Suche in Google Scholar

[14] A. B. Borisov, S. A. Zykov, and M. V. Pavlov, Theore. Math. Phys. 131, 550 (2002).10.1023/A:1015162021255Suche in Google Scholar

Received: 2016-9-27
Accepted: 2016-11-30
Published Online: 2017-1-11
Published in Print: 2017-4-1

©2017 Walter de Gruyter GmbH, Berlin/Boston

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