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TMF, 2015, Volume 185, Number 2, Pages 289–312 (Mi tmf8857)  

This article is cited in 12 scientific papers (total in 12 papers)

The extended $Z_N$-Toda hierarchy

Chuanzhong Li, Jingsong He

Department of Mathematics and Ningbo Collaborative Innovation Center of Nonlinear Hazard System of Ocean and Atmosphere, Ningbo University, Ningbo, China

Abstract: We construct the extended flow equations of a new $Z_N$-Toda hierarchy taking values in a commutative subalgebra $Z_N$ of $gl(N,\mathbb C)$. We give the Hirota bilinear equations and tau function of this new extended $Z_N$-Toda hierarchy. Taking the presence of logarithmic terms into account, we construct some extended vertex operators in generalized Hirota bilinear equations, which might be useful in topological field theory and the Gromov–Witten theory. We present the Darboux transformations and bi-Hamiltonian structure of this hierarchy. Using Hamiltonian tau-symmetry, we obtain another tau function of this hierarchy with some unknown mysterious relation to the tau function derived using the Sato theory.

Keywords: extended $Z_N$-Toda hierarchy, Hirota quadratic equation, Darboux transformation, bi-Hamiltonian structure

DOI: https://doi.org/10.4213/tmf8857

Full text: PDF file (536 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 185:2, 1614–1635

Bibliographic databases:

MSC: 37K05, 37K10, 37K20
Received: 21.01.2015
Revised: 05.03.2015

Citation: Chuanzhong Li, Jingsong He, “The extended $Z_N$-Toda hierarchy”, TMF, 185:2 (2015), 289–312; Theoret. and Math. Phys., 185:2 (2015), 1614–1635

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v185/i2/p289

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ch. Li, “Gauge transformation and symmetries of the commutative multicomponent BKP hierarchy”, J. Phys. A-Math. Theor., 49:1 (2016), 015203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Chuanzhong Li, Jingsong He, “Virasoro symmetry of the constrained multicomponent Kadomtsev–Petviashvili hierarchy and its integrable discretization”, Theoret. and Math. Phys., 187:3 (2016), 871–887  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. T. Song, Ch. Li, J. He, “_orig Constraint on the Multi-Component Ckp Hierarchy and Recursion Operators”, Z. Naturfors. Sect. A-J. Phys. Sci., 71:6 (2016), 487–492  crossref  isi  elib  scopus
    4. Ch. Li, T. Song, “_orig bi-hamiltonian structure of the extended noncommutative toda”, J. Nonlinear Math. Phys., 23:3 (2016), 368–382  crossref  mathscinet  isi  elib  scopus
    5. Ch. Li, A. Meng, “On the full-discrete extended generalised $q$-difference Toda system”, Z. Naturfors. Sect. A-J. Phys. Sci., 72:8 (2017), 703–709  crossref  isi  scopus
    6. N. Wang, Ch. Li, “Quantum torus algebras and B(C)-type Toda systems”, J. Nonlinear Sci., 27:6 (2017), 1957–1970  crossref  mathscinet  zmath  isi  scopus
    7. T. Song, Ch. Li, X. Li, “Gauge transformations of the multi-component BKP and CKP hierarchies”, Mod. Phys. Lett. B, 31:30 (2017), 1750280  crossref  mathscinet  isi  scopus
    8. Ch. Li, “Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries”, J. Geom. Phys., 119 (2017), 103–111  crossref  mathscinet  zmath  isi  scopus
    9. X. Yang, Ch. Li, “Backlund transformations of $Z_n$-sine-Gordon systems”, Mod. Phys. Lett. B, 31:17 (2017), 1750189  crossref  mathscinet  isi  scopus
    10. Ch. Li, “Möbius–Toda hierarchy and its integrability”, Acta Math. Sci., 37:4 (2017), 1151–1161  crossref  mathscinet  zmath  isi
    11. L. Liu, Ch. Li, “Coupled sine-Gordon systems in DNA dynamics”, Adv. Math. Phys., 2018, 4676281  crossref  mathscinet  isi  scopus
    12. H. Wang, Ch. Li, “Backlund transformation of Frobenius Painlevé equations”, Mod. Phys. Lett. B, 32:17 (2018), 1850181  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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