Geodesic
Integrable super extensions of $K(-2,-2)$ equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 405-415 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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