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Symmetric q-deformed KP hierarchy

Abstract

Based on the analytic property of the symmetric q-exponent e q (x), a new symmetric q-deformed Kadomtsev-Petviashvili (q-KP for short) hierarchy associated with the symmetric q-derivative operator q is constructed. Furthermore, the symmetric q-CKP hierarchy and symmetric q-BKP hierarchy are defined. The authors also investigate the additional symmetries of the symmetric q-KP hierarchy.

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Author information

Correspondence to Jingsong He.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11201451, 11271210, 11371278, 11431010), the Erasmus Mundus Action 2 EXPERTS, the SMSTC grant (No. 12XD1405000) and Fundamental Research Funds for the Central Universities.

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Tian, K., He, J. & Su, Y. Symmetric q-deformed KP hierarchy. Chin. Ann. Math. Ser. B 36, 1–10 (2015). https://doi.org/10.1007/s11401-014-0881-5

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Keywords

  • q-Derivative
  • Symmetric q-KP hierarchy
  • Additional symmetries

2000 MR Subject Classification

  • 35Q53
  • 37K05
  • 37K10