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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 210, Number 3, Pages 405–415
DOI: https://doi.org/10.4213/tmf10163 (Mi tmf10163) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Integrable super extensions of $K(-2,-2)$ equation

Hanyu Zhou, Kai Tian

Department of Mathematics, School of Science, China University of Mining and Technology, Beijing, China
Full-text PDF (437 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf10163
Abstract: Two coupled systems involving both bosonic and fermionic fields are proposed as super generalizations of the $K(-2,-2)$ equation $u_t=\partial_x^3(u^{-2}/2)-\partial_x(2u^{-2})$. Linear spectral problems are presented to certify their integrability and lead to infinitely many conservation laws. Based on natural conservation laws, reciprocal transformations are defined that map one super $K(-2,-2)$ equation to Kupershmidt's super modified Korteweg–de Vries (mKdV) equation, and the other super $K(-2,-2)$ equation to the supersymmetric mKdV equation. By means of these connections, bi-Hamiltonian formulations are established for the super $K(-2,-2)$ equations.
Keywords: linear spectral problem, conservation law, reciprocal transformation, Hamiltonian structure.
Funding agency Grant number
National Natural Science Foundation of China 11931017
Fundamental Research Funds for the Central Universities of China 00-800015Z1201
This work was supported by the National Natural Science Foundation of China (NNSFC) (Grant No. 11931017) and the Yue Qi Young Scholar Project, China University of Mining and Technology, Beijing (Grant No. 00-800015Z1201).
Received: 20.08.2021
Revised: 03.12.2021
English version:
Theoretical and Mathematical Physics, 2022, Volume 210, Issue 3, Pages 353–362
DOI: https://doi.org/10.1134/S0040577922030059
Bibliographic databases:
Document Type: Article
MSC: 35Q51, 37K10, 37K35
Language: Russian
Citation: Hanyu Zhou, Kai Tian, “Integrable super extensions of $K(-2,-2)$ equation”, TMF, 210:3 (2022), 405–415; Theoret. and Math. Phys., 210:3 (2022), 353–362
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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