Abstract
We construct a solution expressed in terms of Schur Q-functions of a strongly coupled B-type Kadomtsev-Petviashvili hierarchy. As a generalization of these functions, we introduce universal characters satisfying the bilinear equations of a new infinite-dimensional integrable system called the strongly coupled B-type universal character hierarchy.
Similar content being viewed by others
References
E. Date, M. Kashiwara, M. Jimbo, and T. Miwa, “Transformation groups for soliton equations,” in: Non-Linear Integrable Systems — Classical Theory and Quantum Theory (Kyoto, Japan, 13–16 May 1981, M. Satō, M. Jimbo, and T. Miwa, eds.), World Scientific, Singapore (1983), pp. 39–119.
T. Tsuda, “Universal characters and an extension of the KP hierarchy,” Commun. Math. Phys., 248, (501–526) (2004).
T. Tsuda, “From KP/UC hierarchies to Painlevé equations,” Internat. J. Math., 23, (1250010) (2012).
I. A. B. Strachan and D. F. Zuo, “Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy,” J. Math. Phys., 56, (113509) (2015); arXiv:1511.05245v1 [math-ph] (2015).
Chuanzhong Li and Jingsong He, “Virasoro symmetry of the constrained multicomponent Kadomtsev-Petviashvili hierarchy and its integrable discretization,” Theor. Math. Phys., 187, (871–887) (2016).
C. Z. Li, “Gauge transformation and symmetries of the commutative multicomponent BKP hierarchy,” J. Phys. A: Math. Theor., 49, (015203) (2016).
X. P. Yang and C. Z. Li, “Bäcklund transformations of Z n-sine-Gordon systems,” Modern Phys. Lett. B, 31, (1750189) (2017); arXiv:1704.04412v1 [nlin.SI] (2017).
H. F. Wang and C. Z. Li, “Affine Weyl group symmetries of Frobenius Painlevé equations,” Math. Methods Appl. Sci. (to appear).
C. Z. Li, “Coupled universal characters and coupled integrable hierarchies,” Lett. Math. Phys. (submitted).
Y. Ogawa, “Generalized Q-Functions and UC Hierarchy of B-Type,” Tokyo J. Math., 32, (349–380) (2009).
T. Tsuda, “On an integrable system of q-difference equations satisfied by the universal characters: Its Lax formalism and an application to q-Painlevé equations,” Commun. Math. Phys., 293, 347–359 (2010); arXiv:0901.3900v2 [nlin.SI] (2009).
K. Sawada and T. Kotera, “A method for finding N-soliton solutions of the K.d.V. equation and K.d.V.-like equation,” Prog. Theor. Phys., 51, (1355–1367) (1974).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest. The author declares no conflicts of interest.
Additional information
This research is supported by the National Natural Science Foundation of China (Grant No. 11571192) and K. C. Wong Magna Fund in Ningbo University.
Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 3, pp. 371–381, December, 2019.
Rights and permissions
About this article
Cite this article
Li, C. Strongly Coupled B-Type Universal Characters and Hierarchies. Theor Math Phys 201, 1732–1741 (2019). https://doi.org/10.1134/S0040577919120067
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577919120067