Integrable super extensions of $K(-2,-2)$ equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 405-415
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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.
@article{TMF_2022_210_3_a4,
author = {Hanyu Zhou and Kai Tian},
title = {Integrable super extensions of $K(-2,-2)$ equation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {405--415},
publisher = {mathdoc},
volume = {210},
number = {3},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a4/}
}
Hanyu Zhou; Kai Tian. Integrable super extensions of $K(-2,-2)$ equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 405-415. http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a4/